Uniformly accelerated motion is a fundamental concept in kinematics, essential for understanding how objects move under constant acceleration. This topic is pivotal in the curriculum for the AS & A Level Physics (9702) board exams, providing students with the tools to analyze and solve real-world physics problems involving acceleration. Mastery of uniformly accelerated motion forms the foundation for advanced studies in mechanics and other related fields.

Key Concepts

1. Understanding Uniformly Accelerated Motion

Uniformly accelerated motion refers to the motion of an object with a constant acceleration. Unlike constant velocity, where speed and direction remain unchanged, uniformly accelerated motion involves a consistent change in the velocity of the object over time. This type of motion is described by specific kinematic equations that relate displacement, velocity, acceleration, and time.

2. Fundamental Equations of Motion

The core equations governing uniformly accelerated motion are derived under the assumption of constant acceleration. These equations allow for the calculation of various parameters involved in the motion of objects:

First Equation of Motion: Relates initial velocity, final velocity, acceleration, and time.
$$v = u + at$$
Where:
- $v$ = final velocity
- $u$ = initial velocity
- $a$ = acceleration
- $t$ = time
Second Equation of Motion: Relates displacement, initial velocity, time, and acceleration.
$$s = ut + \frac{1}{2}at^2$$
Where:
- $s$ = displacement
- $u$ = initial velocity
- $t$ = time
- $a$ = acceleration
Third Equation of Motion: Relates final velocity, initial velocity, acceleration, and displacement.
$$v^2 = u^2 + 2as$$
Where:
- $v$ = final velocity
- $u$ = initial velocity
- $a$ = acceleration
- $s$ = displacement

3. Graphical Representation of Motion

Graphical analysis is a powerful tool in understanding uniformly accelerated motion. The main graphs used are:

Velocity-Time (v-t) Graph: A straight line with a slope equal to acceleration. The area under the graph represents displacement.
Displacement-Time (s-t) Graph: A parabola representing the relationship between displacement and time under constant acceleration.
Acceleration-Time (a-t) Graph: A horizontal line indicating constant acceleration.

4. Free-Body Diagrams and Forces

Analyzing forces acting on an object is crucial for solving problems in uniformly accelerated motion. A free-body diagram helps visualize these forces, enabling the application of Newton's Second Law:

$$F = ma$$

Where:

$F$ = net force
$m$ = mass of the object
$a$ = acceleration

5. Solving Kinematic Problems

To solve problems involving uniformly accelerated motion, follow these steps:

Identify the known and unknown quantities.
Choose the appropriate equation of motion.
Substitute the known values and solve for the unknown.
Check the results for consistency and correctness.

Example: A car accelerates from rest at a rate of $2 \, m/s^2$ for $5$ seconds. Find its final velocity and displacement.

Using the first equation of motion: $$v = u + at = 0 + (2)(5) = 10 \, m/s$$ Using the second equation of motion: $$s = ut + \frac{1}{2}at^2 = 0 + \frac{1}{2}(2)(5)^2 = 25 \, m$$

6. Relative Motion and Frame of Reference

Understanding relative motion is essential when analyzing uniformly accelerated motion from different frames of reference. The laws of physics, including the equations of motion, hold true in all inertial frames. However, acceleration is not relative in the same way velocity is, and must be considered accordingly.

7. Dimensional Analysis and Units

Ensuring consistency in units is vital for accurate problem-solving. Common units used in uniformly accelerated motion include meters (m) for displacement, seconds (s) for time, and meters per second squared ($m/s^2$) for acceleration. Dimensional analysis helps verify the correctness of equations and calculations.

Advanced Concepts

1. Derivation of Equations of Motion

To gain a deeper understanding of uniformly accelerated motion, it's beneficial to derive the fundamental equations from basic principles. Starting with the definition of acceleration: $$a = \frac{dv}{dt}$$ Integrating with respect to time, we obtain the first equation of motion: $$v = u + at$$ Next, displacement can be found by integrating velocity: $$s = \int v \, dt = ut + \frac{1}{2}at^2$$ Finally, eliminating time between the first two equations leads to the third equation of motion: $$v^2 = u^2 + 2as$$ These derivations highlight the interconnectedness of the kinematic variables and provide a solid foundation for solving more complex problems.

2. Projectile Motion and Uniformly Accelerated Motion

Projectile motion is an application of uniformly accelerated motion in two dimensions. By decomposing the motion into horizontal and vertical components, students can analyze the trajectory of projectiles. The horizontal motion occurs with constant velocity (assuming air resistance is negligible), while the vertical motion is uniformly accelerated under gravity ($g \approx 9.81 \, m/s^2$).

Example: A ball is thrown horizontally with a velocity of $10 \, m/s$ from a height of $20 \, m$. Calculate the time it takes to hit the ground and the horizontal distance traveled.

Time to fall: $$s = \frac{1}{2}gt^2 \Rightarrow 20 = \frac{1}{2}(9.81)t^2 \Rightarrow t^2 = \frac{40}{9.81} \Rightarrow t \approx 2.02 \, s$$ Horizontal distance: $$d = vt = 10 \times 2.02 \approx 20.2 \, m$$

3. Relative Acceleration in Non-Inertial Frames

When analyzing motion from a non-inertial (accelerating) frame of reference, fictitious forces must be introduced to account for the observed motion. This concept extends uniformly accelerated motion to more complex scenarios where the observer is accelerating relative to an inertial frame.

Example: Consider a train accelerating at $a$. A passenger inside the train perceives a fictitious force acting on objects opposite to the direction of acceleration. This leads to apparent trajectories that differ from those observed in an inertial frame.

4. Applications in Engineering and Technology

Uniformly accelerated motion principles are extensively applied in various engineering fields. For instance, in mechanical engineering, understanding acceleration is crucial for designing vehicle systems, ensuring safety and performance. In aerospace engineering, these concepts are vital for calculating trajectories and optimizing flight paths.

Case Study: The design of roller coasters relies on uniformly accelerated motion to ensure riders experience thrilling yet safe accelerations during climbs and drops. Engineers use precise calculations to determine the necessary slopes and curves.

5. Integration with Energy Concepts

Uniformly accelerated motion is closely linked with work and energy principles. Kinetic energy changes in accelerated motion can be analyzed using the work-energy theorem: $$W = \Delta KE = \frac{1}{2}mv^2 - \frac{1}{2}mu^2$$ This integration provides a comprehensive understanding of how forces and motion interact energetically.

6. Solving Complex Multi-Step Problems

Advanced problem-solving involves tackling multi-step scenarios where multiple kinematic equations and concepts are applied simultaneously. These problems often require breaking down the motion into simpler parts, solving sequentially, and integrating results to find the final solution.

Example: A car accelerates uniformly from rest to a speed of $30 \, m/s$ over a distance of $450 \, m$. Determine the acceleration and the time taken.

Using the third equation of motion: $$v^2 = u^2 + 2as \Rightarrow (30)^2 = 0 + 2a(450) \Rightarrow 900 = 900a \Rightarrow a = 1 \, m/s^2$$ Using the first equation of motion: $$v = u + at \Rightarrow 30 = 0 + (1)t \Rightarrow t = 30 \, s$$

7. Motion Under Variable Acceleration

While uniformly accelerated motion assumes constant acceleration, real-world scenarios often involve variable acceleration. Understanding the deviations from uniform acceleration requires calculus-based kinematics, where acceleration is a function of time or displacement.

Example: An object experiences acceleration proportional to its velocity, $a = k v$. Solving the differential equation: $$\frac{dv}{dt} = k v \Rightarrow \int \frac{1}{v} dv = \int k \, dt \Rightarrow \ln v = kt + C$$ Exponentiating both sides: $$v = Ce^{kt}$$ This solution demonstrates exponential growth or decay in velocity, differing from the linear relationship in uniform acceleration.

8. Dimensional Consistency and Verification

Ensuring dimensional consistency in equations is critical for validating solutions in uniformly accelerated motion. Each term in an equation must have consistent units, enabling the detection of errors in derivations and calculations.

Example: In the equation $s = ut + \frac{1}{2}at^2$, the units on both sides must match:

$s$: meters (m)
$ut$: $(m/s)(s) = m$
$\frac{1}{2}at^2$: $(m/s^2)(s^2) = m$

Thus, the equation is dimensionally consistent.

9. Incorporating Air Resistance and Other Forces

In real-life applications, additional forces like air resistance affect uniformly accelerated motion. While basic kinematic equations assume negligible air resistance, advanced problems incorporate these forces to model more accurate scenarios.

Example: A skydiver falling with air resistance experiences a net acceleration that decreases over time, approaching terminal velocity where gravitational force balances air resistance: $$mg = kv$$ $$v_{terminal} = \frac{mg}{k}$$

10. Extension to Two-Dimensional Motion

Uniformly accelerated motion can be extended to two dimensions, involving both horizontal and vertical components. This is crucial for analyzing projectile motion, where horizontal motion is typically uniform, and vertical motion is uniformly accelerated due to gravity.

Example: A projectile launched at an angle $\theta$ with initial speed $v_0$ has:

Horizontal velocity: $v_{x} = v_0 \cos \theta$ (constant)
Vertical velocity: $v_{y} = v_0 \sin \theta - gt$ (uniformly accelerated)

Comparison Table

Aspect	Uniformly Accelerated Motion	Constant Velocity Motion
Acceleration	Constant and non-zero	Zero
Velocity	Changes uniformly over time	Remains constant
Displacement	Quadratic relation with time	Linear relation with time
Graph Representation	Parabolic displacement-time graph	Straight line displacement-time graph
Applicability	Free-fall, accelerating cars	Objects moving at constant speed
Equations Used	Equations of motion with acceleration	Basic distance = speed × time

Summary and Key Takeaways

Uniformly accelerated motion involves constant acceleration, affecting velocity and displacement over time.
Key equations of motion facilitate the analysis and solution of various kinematic problems.
Advanced concepts extend basic principles to complex scenarios, including projectile motion and non-inertial frames.
Dimensional analysis and graphical representations are essential tools for verifying and understanding motion.
Applications span multiple fields, highlighting the practical significance of uniformly accelerated motion.

Examiner Tip

Tips

1. Memorize the Kinematic Equations: Having the four main equations at your fingertips saves time during exams.
2. Draw Free-Body Diagrams: Visualizing forces helps in understanding the problem and applying Newton's laws correctly.
3. Pay Attention to Sign Conventions: Always define your positive direction at the start to maintain consistency in calculations.
4. Practice Dimensional Analysis: Ensure that your equations are dimensionally consistent to catch potential errors early.
5. Break Down Complex Problems: Tackle multi-step problems by solving smaller parts sequentially, which makes them more manageable.

Did You Know

Did you know that uniformly accelerated motion principles are crucial in designing amusement park rides? Engineers use these concepts to ensure safety and optimal thrill by calculating the required acceleration and deceleration rates. Additionally, the Apollo moon missions relied on uniformly accelerated motion equations to plot the spacecraft's trajectory, ensuring precise landings on the lunar surface. Understanding these applications highlights the real-world significance of mastering uniformly accelerated motion in physics.

Common Mistakes

1. Ignoring Direction: Students often overlook the direction of acceleration and velocity, leading to incorrect sign conventions. For example, if an object decelerates, acceleration should be negative.
Incorrect Approach: Using positive acceleration for deceleration.
Correct Approach: Assign a negative value to acceleration when the object is slowing down.

2. Misapplying Equations: Selecting the wrong kinematic equation based on the given information can result in errors.
Incorrect Approach: Using $v = u + at$ when time is not provided.
Correct Approach: Choose an equation that includes the known variables, such as $v^2 = u^2 + 2as$ if time is unknown.

3. Unit Inconsistencies: Failing to convert units properly can lead to incorrect answers.
Incorrect Approach: Mixing meters and centimeters without conversion.
Correct Approach: Convert all measurements to consistent units before performing calculations.

FAQ

1. What is uniformly accelerated motion?

Uniformly accelerated motion refers to the movement of an object with a constant acceleration, meaning its velocity changes at a steady rate over time.

2. How do you determine which kinematic equation to use?

Choose the equation that includes the variables you know and the one you need to find. Familiarity with each equation's components is key to selecting the right one.

3. What is the difference between acceleration and velocity?

Velocity is the speed of an object in a given direction, while acceleration is the rate at which the velocity of the object changes over time.

4. Can acceleration be negative?

Yes, negative acceleration indicates that the object is slowing down, also known as deceleration.

5. How does air resistance affect uniformly accelerated motion?

Air resistance introduces additional forces that can alter the acceleration, making it non-uniform. In basic kinematic equations, air resistance is typically neglected for simplicity.

6. What is terminal velocity?

Terminal velocity is the constant speed achieved by an object when the force of gravity is balanced by air resistance, resulting in zero net acceleration.

1. Capacitance

1.1 Energy Stored in a Capacitor

1.1.1 Determine electric potential energy stored in a capacitor from the area under the potential–charge g

1.1.2 Recall and use W = ½QV = ½CV²

1.2 Discharging a Capacitor

1.2.1 Analyze graphs of potential difference, charge, and current during capacitor discharge

1.2.2 Recall and use τ = RC for the time constant during discharge

1.2.3 Use equations of the form x = x₀e^(-t / RC) for current, charge, or potential during discharge

1.3 Capacitors and Capacitance

1.3.1 Define capacitance for isolated spherical conductors and parallel plate capacitors

1.3.2 Recall and use C = Q / V

1.3.3 Derive formulae for combined capacitance of capacitors in series and parallel

1.3.4 Use capacitance formulae for capacitors in series and parallel

2. Nuclear Physics

2.1 Mass Defect and Nuclear Binding Energy

2.1.1 Sketch the variation of binding energy per nucleon with nucleon number

2.1.2 Explain nuclear fusion and nuclear fission

2.1.3 Calculate the energy released in nuclear reactions using E = c²∆m

2.1.4 Understand the equivalence between energy and mass (E = mc²)

2.1.5 Define and use the terms mass defect and binding energy

2.2 Radioactive Decay

2.2.1 Understand that fluctuations in count rate provide evidence for random decay

2.2.2 Understand that radioactive decay is spontaneous and random

2.2.3 Define activity and decay constant, and recall A = λN

2.2.4 Define half-life

2.2.5 Use λ = 0.693 / t₁/₂ for the half-life relationship

2.2.6 Understand exponential decay and use the relationship x = x₀e^(-λt)

3. Kinematics

3.1 Equations of Motion

3.1.1 Define and use distance, displacement, speed, velocity, acceleration

3.1.2 Use graphical methods to represent motion

3.1.3 Determine displacement from velocity–time graph

3.1.4 Determine velocity using gradient of displacement–time graph

3.1.5 Determine acceleration using gradient of velocity–time graph

3.1.6 Derive equations for uniformly accelerated motion

3.1.7 Solve problems of uniformly accelerated motion

3.1.8 Describe experiment to determine acceleration due to gravity

3.1.9 Explain motion with uniform velocity and perpendicular acceleration

4. Deformation of Solids

4.1 Stress and Strain

4.1.1 Understand and use the terms load, extension, compression, and limit of proportionality

4.1.2 Recall and use Hooke’s law

4.1.3 Recall and use the formula for spring constant k = F / x

4.1.4 Define and use terms stress, strain, and Young's modulus

4.1.5 Describe an experiment to determine Young’s modulus

4.1.6 Understand deformation caused by tensile or compressive forces

4.2 Elastic and Plastic Behaviour

4.2.1 Understand elastic and plastic deformation and elastic limit

4.2.2 Understand area under the force–extension graph as work done

4.2.3 Calculate elastic potential energy using EP = ½kx²

5. Gravitational Fields

5.1 Gravitational Field of a Point Mass

5.1.1 Understand that g is approximately constant for small height changes near Earth's surface

5.1.2 Recall and use g = GM / r²

5.1.3 Derive and use g = GM / r² for gravitational field strength

5.2 Gravitational Potential

5.2.1 Define gravitational potential as work done per unit mass in bringing a test mass from infinity

5.2.2 Use ϕ = -GM / r for gravitational potential due to a point mass

5.2.3 Use EP = -GMm / r for gravitational potential energy between two point masses

5.3 Gravitational Field

5.3.1 Define gravitational field as force per unit mass

5.3.2 Represent a gravitational field using field lines

5.4 Gravitational Force Between Point Masses

5.4.1 For point outside uniform sphere, treat mass as a point mass at its center

5.4.2 Analyze circular orbits in gravitational fields

5.4.3 Recall and use Newton's law of gravitation F = Gm₁m₂ / r²

6. Electricity

6.1 Resistance and Resistivity

6.1.1 Understand that the resistance of a thermistor decreases as temperature increases

6.1.2 Define resistance and recall and use V = IR

6.1.3 Sketch I–V characteristics for metallic conductor, semiconductor diode, and filament lamp

6.1.4 Explain that the resistance of a filament lamp increases as current increases

6.1.5 State Ohm’s law and recall and use R = ρL / A

6.1.6 Understand that the resistance of an LDR decreases as light intensity increases

6.2 Electric Current

6.2.1 Understand that an electric current is a flow of charge carriers

6.2.2 Understand that the charge on charge carriers is quantised

6.2.3 Recall and use Q = It

6.2.4 Use I = Anvq for current-carrying conductors

6.3 Potential Difference and Power

6.3.1 Define potential difference as energy transferred per unit charge

6.3.2 Recall and use V = W / Q

6.3.3 Recall and use P = VI, P = I²R, P = V² / R

7. D.C. Circuits

7.1 Practical Circuits

7.1.1 Recall and use the circuit symbols in the syllabus

7.1.2 Draw and interpret circuit diagrams using circuit symbols

7.1.3 Define electromotive force (e.m.f.) of a source as energy transferred per unit charge

7.1.4 Distinguish between e.m.f. and potential difference (p.d.)

7.1.5 Understand the effects of internal resistance on terminal potential difference

7.2 Kirchhoff’s Laws

7.2.1 Recall Kirchhoff’s first law: conservation of charge

7.2.2 Recall Kirchhoff’s second law: conservation of energy

7.2.3 Derive the formula for combined resistance of resistors in series using Kirchhoff’s laws

7.2.4 Use the formula for combined resistance of resistors in series

7.2.5 Derive the formula for combined resistance of resistors in parallel using Kirchhoff’s laws

7.2.6 Use the formula for combined resistance of resistors in parallel

7.2.7 Use Kirchhoff’s laws to solve simple circuit problems

7.3 Potential Dividers

7.3.1 Understand the principle of a potential divider circuit

7.3.2 Recall and use the principle of the potentiometer for comparing potential differences

7.3.3 Understand the use of a galvanometer in null methods

7.3.4 Explain the use of thermistors and LDRs in potential dividers to provide a potential dependent on te

8. Thermal Equilibrium

8.1 Thermal Energy Transfer

8.1.1 Understand that thermal energy transfers from higher to lower temperature

8.1.2 Understand that regions of equal temperature are in thermal equilibrium

9. Temperature Scales

9.1 Temperature Measurement

9.1.1 Understand physical properties that vary with temperature (e.g., density, gas volume, resistance)

9.1.2 Convert temperatures between Kelvin and Celsius, and recall T(K) = θ(°C) + 273.15

10. Magnetic Fields

10.1 Concept of a Magnetic Field

10.1.1 Understand that a magnetic field is a field of force produced by moving charges or permanent magnets

10.1.2 Represent a magnetic field using field lines

10.2 Force on a Current-Carrying Conductor

10.2.1 Understand that a force acts on a current-carrying conductor in a magnetic field

10.2.2 Recall and use F = BIL sin θ for the force on a current-carrying conductor in a magnetic field

10.2.3 Define magnetic flux density as the force per unit current per unit length on a wire at right angles

10.3 Force on a Moving Charge

10.3.1 Determine the direction of the force on a charge moving in a magnetic field

10.3.2 Recall and use F = BQv sin θ for the force on a moving charge in a magnetic field

10.3.3 Understand the origin of the Hall voltage and use the expression VH = BI / (ntq) for the Hall voltag

10.3.4 Understand the use of a Hall probe to measure magnetic flux density

10.4 Magnetic Fields Due to Currents

10.4.1 Sketch magnetic field patterns due to currents in a straight wire, flat coil, and solenoid

10.4.2 Understand that magnetic field in a solenoid is increased by a ferrous core

10.4.3 Explain the origin of forces between current-carrying conductors and determine the direction of the

10.5 Electromagnetic Induction

10.5.1 Define magnetic flux as the product of magnetic flux density and area perpendicular to flux directio

10.5.2 Recall and use Φ = BA for magnetic flux

10.5.3 Understand and use the concept of magnetic flux linkage

10.5.4 Explain experiments that show changing magnetic flux induces an e.m.f.

10.5.5 Recall and use Faraday’s and Lenz’s laws of electromagnetic induction

11. Specific Heat Capacity and Latent Heat

11.1 Specific Heat Capacity

11.1.1 Define and use specific heat capacity

11.2 Latent Heat

11.2.1 Define and use specific latent heat; distinguish between fusion and vaporisation

12. Dynamics

12.1 Momentum and Newton’s Laws of Motion

12.1.1 Mass resists change in motion

12.1.2 Recall F = ma and solve related problems

12.1.3 Define and use linear momentum

12.1.4 Force as rate of change of momentum

12.1.5 State and apply Newton’s laws

12.1.6 Describe weight as effect of gravitational field

12.1.7 Weight of an object is mass × gravitational acceleration

12.2 Non-uniform Motion

12.2.1 Understand frictional and drag forces

12.2.2 Describe motion in uniform gravitational field with air resistance

12.2.3 Objects moving against resistive force may reach terminal velocity

12.3 Linear Momentum and its Conservation

12.3.1 State conservation of momentum

12.3.2 Apply conservation of momentum to solve problems

12.3.3 For elastic collision, kinetic energy and relative speed are conserved

12.3.4 Momentum is conserved, but some kinetic energy may change

13. Medical Physics

13.1 Production and Use of Ultrasound

13.1.1 Understand that a piezo-electric crystal changes shape when a p.d. is applied and generates an e.m.f

13.1.2 Understand how ultrasound waves are generated and detected by a piezoelectric transducer

13.1.3 Understand how ultrasound reflection at boundaries provides diagnostic information about internal st

13.1.4 Define specific acoustic impedance as Z = ρc

13.1.5 Use the equation IR / I₀ = (Z₁ – Z₂)² / (Z₁ + Z₂)² for the intensity reflection coefficient

13.2 Production and Use of X-rays

13.2.1 Explain that X-rays are produced by electron bombardment of a metal target and calculate the minimum

13.2.2 Understand the use of X-rays in imaging internal body structures and the term 'contrast' in X-ray im

13.2.3 Recall and use I = I₀e^(-μx) for the attenuation of X-rays in matter

13.2.4 Understand how computed tomography (CT) produces 3D images by combining multiple 2D X-ray images

13.3 PET Scanning

13.3.1 Understand that a tracer contains radioactive nuclei and is introduced into the body for imaging

13.3.2 Understand that β+ decay is used in positron emission tomography (PET)

13.3.3 Understand that annihilation occurs when a particle interacts with its antiparticle, conserving mass

13.3.4 Explain how gamma-ray photons from annihilation are detected to create an image of tracer concentrat

14. Waves

14.1 Progressive Waves

14.1.1 Describe wave motion in ropes, springs, and ripple tanks

14.1.2 Understand and use the terms displacement, amplitude, phase difference, period, frequency, wavelengt

14.1.3 Use time-base and y-gain on a cathode-ray oscilloscope (CRO) to determine frequency and amplitude

14.1.4 Derive and use v = f λ for the wave equation

14.1.5 Recall and use v = f λ

14.1.6 Understand energy transfer by a progressive wave

14.1.7 Recall and use intensity = power / area, intensity ∝ (amplitude)²

14.2 Transverse and Longitudinal Waves

14.2.1 Compare transverse and longitudinal waves

14.2.2 Analyze and interpret graphical representations of transverse and longitudinal waves

14.3 Doppler Effect for Sound Waves

14.3.1 Understand the change in frequency when a sound source moves relative to a stationary observer

14.3.2 Use the expression f₀ = fₛ(v / (v ± vₛ)) for the observed frequency

14.4 Electromagnetic Spectrum

14.4.1 State all electromagnetic waves are transverse waves traveling at the same speed in free space

14.4.2 Recall the range of wavelengths from radio waves to γ-rays

14.4.3 Recall that wavelengths 400–700 nm are visible to the human eye

14.5 Polarisation

14.5.1 Understand that polarisation is a phenomenon associated with transverse waves

14.5.2 Recall and use Malus's law (I = I₀ cos²θ) to calculate intensity of a plane-polarised wave after pas

15. The Mole

15.1 The Mole

15.1.1 Understand that amount of substance is an SI base quantity with the unit mol

15.1.2 Use molar quantities where one mole contains Avogadro's constant of particles

16. Equation of State

16.1 Ideal Gas Law

16.1.1 Understand that a gas obeying pV ∝ T is an ideal gas

16.1.2 Recall and use the equation pV = nRT for an ideal gas

16.1.3 Recall pV = NkT, where N = number of molecules and k is Boltzmann constant

16.1.4 Use the relationship k = R / NA

17. Kinetic Theory of Gases

17.1 Kinetic Theory

17.1.1 State the basic assumptions of the kinetic theory of gases

17.1.2 Explain pressure exerted by a gas due to molecular movement

17.1.3 Derive and use pV = (3/2)NmkT for pressure of a gas

17.1.4 Compare pV = (3/2)NmkT with pV = NkT to deduce average kinetic energy of a molecule

18. Particle Physics

18.1 Atoms, Nuclei and Radiation

18.1.1 Infer the existence and small size of the nucleus from α-particle scattering

18.1.2 Describe the nuclear atom model: protons, neutrons, and electrons

18.1.3 Distinguish between nucleon number and proton number

18.1.4 Understand isotopes as forms of the same element with different neutrons

18.1.5 Use the notation AZX for nuclides representation

18.1.6 Understand conservation of nucleon number and charge in nuclear processes

18.1.7 Describe the composition, mass, and charge of α-, β-, and γ-radiations

18.1.8 Understand antiparticles and positrons as antiparticles of electrons

18.1.9 State that (electron) antineutrinos are produced during β- decay and neutrinos during β+ decay

18.1.10 Represent α- and β-decay using radioactive decay equations

18.1.11 Use unified atomic mass unit (u) for mass

18.2 Fundamental Particles

18.2.1 Understand quarks as fundamental particles with six flavours

18.2.2 Understand hadrons as baryons (three quarks) or mesons (one quark and one antiquark)

18.2.3 Describe changes in quark composition during β- and β+ decay

18.2.4 Describe protons and neutrons as composed of quarks

18.2.5 Recall and use the charge of each quark and its respective antiquark

18.2.6 Recall electrons and neutrinos as fundamental particles (leptons)

19. Internal Energy

19.1 Internal Energy

19.1.1 Understand that internal energy is the sum of kinetic and potential energies of molecules in a syste

19.1.2 Relate rise in temperature to an increase in internal energy

20. Forces, Density and Pressure

20.1 Turning Effects of Forces

20.1.1 Weight acts at a single point: centre of gravity

20.1.2 Define and apply the moment of a force

20.1.3 Understand the concept of a couple

20.1.4 Define and apply torque of a couple

20.2 Equilibrium of Forces

20.2.1 State and apply the principle of moments

20.2.2 System in equilibrium has no resultant force or torque

20.2.3 Use a vector triangle to represent coplanar forces in equilibrium

20.3 Density and Pressure

20.3.1 Define and use density

20.3.2 Define and use pressure

20.3.3 Derive equation for hydrostatic pressure ∆p = ρg∆h

20.3.4 Use the equation ∆p = ρg∆h

20.3.5 Understand upthrust as the effect of hydrostatic pressure

20.3.6 Calculate upthrust using F = ρgV (Archimedes' principle)

21. Astronomy and Cosmology

21.1 Standard Candles

21.1.1 Understand luminosity as the total power radiated by a star

21.1.2 Recall and use the inverse square law F = L / (4πd²) for radiant flux intensity

21.1.3 Understand that an object with known luminosity is a standard candle

21.1.4 Use standard candles to determine distances to galaxies

21.2 Stellar Radii

21.2.1 Recall and use Wien’s displacement law λmax ∝ 1 / T to estimate the surface temperature of a star

21.2.2 Use Stefan–Boltzmann law L = 4πσr²T⁴

21.2.3 Use Wien’s law and Stefan–Boltzmann law to estimate the radius of a star

21.3 Hubble’s Law and Big Bang Theory

21.3.1 Understand redshift and the increase in wavelength of light from distant objects

21.3.2 Use ∆λ / λ = ∆f / f = v / c for redshift

21.3.3 Explain why redshift suggests the Universe is expanding

21.3.4 Recall and use Hubble’s law v = H₀d to explain the Big Bang theory

22. First Law of Thermodynamics

22.1 First Law

22.1.1 Recall and use W = p∆V for work done when the volume of a gas changes at constant pressure

22.1.2 Understand the difference between work done by a gas and work done on a gas

22.1.3 Recall and use the first law of thermodynamics: ∆U = q + W

23. Alternating Currents

23.1 Characteristics of Alternating Currents

23.1.1 Understand and use terms period, frequency, and peak value for alternating current or voltage

23.1.2 Use x = x₀ sin(ωt) for sinusoidal alternating current or voltage

23.1.3 Recall that the mean power in a resistive load is half the maximum power for sinusoidal current

23.1.4 Distinguish between root-mean-square (r.m.s.) and peak values and recall I₀r.m.s = I₀ / √2 and V₀r.m

23.2 Rectification and Smoothing

23.2.1 Distinguish graphically between half-wave and full-wave rectification

23.2.2 Explain the use of a single diode for half-wave rectification

23.2.3 Explain the use of four diodes (bridge rectifier) for full-wave rectification

23.2.4 Analyze the effect of a capacitor in smoothing, including the effect of capacitance and load resista

24. Superposition

24.1 Stationary Waves

24.1.1 Explain and use the principle of superposition

24.1.2 Understand experiments demonstrating stationary waves using microwaves, stretched strings, and air c

24.1.3 Explain the formation of stationary waves using graphical methods and identify nodes and antinodes

24.1.4 Determine wavelength from the positions of nodes or antinodes

24.2 Diffraction

24.2.1 Explain diffraction and show understanding of related experiments

24.2.2 Understand the effect of gap width relative to wavelength in diffraction experiments

24.3 Interference

24.3.1 Understand the terms interference and coherence

24.3.2 Demonstrate two-source interference using water waves, sound, light, and microwaves

24.3.3 Understand the conditions required for two-source interference fringes

24.3.4 Recall and use λ = ax / D for double-slit interference with light

24.4 Diffraction Grating

24.4.1 Recall and use d sin θ = nλ for diffraction grating calculations

24.4.2 Describe the use of a diffraction grating to determine the wavelength of light

25. Simple Harmonic Oscillations

25.1 Simple Harmonic Motion

25.1.1 Understand and use terms displacement, amplitude, period, frequency, angular frequency, and phase di

25.1.2 Understand that simple harmonic motion occurs when acceleration is proportional to displacement from

25.1.3 Use a = -ω²x and recall x = x₀ sin(ωt) as the solution

25.1.4 Use v = v₀ cos(ωt) and v = ±ω√(x₀² - x²) for velocity

26. Energy in Simple Harmonic Motion

26.1 Energy in SHM

26.1.1 Describe the interchange between kinetic and potential energy during SHM

26.1.2 Recall and use E = ½mω²x₀² for the total energy of a system undergoing SHM

27. Quantum Physics

27.1 Energy and Momentum of a Photon

27.1.1 Understand that electromagnetic radiation has a particulate nature

27.1.2 Recall and use E = hf for the energy of a photon

27.1.3 Use the electronvolt (eV) as a unit of energy

27.1.4 Understand that a photon has momentum and use p = E / c for photon momentum

27.2 Photoelectric Effect

27.2.1 Understand that photoelectrons are emitted from a metal surface when illuminated by electromagnetic

27.2.2 Understand and use the terms threshold frequency and threshold wavelength

27.2.3 Explain photoelectric emission in terms of photon energy and work function

27.2.4 Recall and use hf = Φ + ½mv² for the maximum kinetic energy of photoelectrons

27.2.5 Explain why the maximum kinetic energy of photoelectrons is independent of intensity, while current

27.3 Wave-Particle Duality

27.3.1 Understand that the photoelectric effect shows the particulate nature of light, while diffraction sh

27.3.2 Describe and interpret electron diffraction as evidence for the wave nature of particles

27.3.3 Understand the de Broglie wavelength as the wavelength associated with a moving particle

27.3.4 Recall and use λ = h / p for de Broglie wavelength

27.4 Energy Levels in Atoms and Line Spectra

27.4.1 Understand discrete electron energy levels in atoms (e.g., atomic hydrogen)

27.4.2 Understand the appearance and formation of emission and absorption line spectra

27.4.3 Recall and use hf = E₁ – E₂ for the energy difference between electron energy levels

28. Damped and Forced Oscillations, Resonance

28.1 Damped Oscillations

28.1.1 Understand that damping occurs due to resistive forces

28.1.2 Understand the types of damping: light, critical, and heavy damping

28.2 Resonance

28.2.1 Understand that resonance occurs when an oscillating system is forced to oscillate at its natural fr

29. Work, Energy and Power

29.1 Energy Conservation

29.1.1 Understand the concept of work, and recall W = F × s

29.1.2 Apply the principle of conservation of energy

29.1.3 Understand efficiency as useful energy output / total energy input

29.1.4 Use efficiency concept to solve problems

29.1.5 Define power as work done per unit time

29.1.6 Solve problems using P = W / t

29.1.7 Derive P = Fv and solve problems

29.2 Gravitational Potential Energy and Kinetic Energy

29.2.1 Derive ∆EP = mg∆h for gravitational potential energy changes

29.2.2 Recall and use ∆EP = mg∆h for gravitational potential energy changes

29.2.3 Derive EK = ½mv² for kinetic energy

29.2.4 Recall and use EK = ½mv² for kinetic energy

30. Electric Fields

30.1 Electric Fields and Field Lines

30.1.1 Understand that an electric field is a field of force and define it as force per unit positive charg

30.1.2 Represent an electric field using field lines

30.2 Uniform Electric Fields

30.2.1 Recall and use E = ∆V / ∆d to calculate electric field strength between charged parallel plates

30.2.2 Describe the effect of a uniform electric field on the motion of charged particles

30.3 Electric Force Between Point Charges

30.3.1 Understand that, for a point outside a spherical conductor, the charge may be considered a point mas

30.3.2 Recall and use Coulomb’s law F = Q₁Q₂ / (4πε₀r²) for the force between two point charges

30.4 Electric Field of a Point Charge

30.4.1 Recall and use E = Q / (4πε₀r²) for the electric field strength due to a point charge

30.5 Electric Potential

30.5.1 Define electric potential as work done per unit positive charge in bringing a test charge from infin

30.5.2 Recall and use V = Q / (4πε₀r) for electric potential due to a point charge

30.5.3 Understand how electric potential leads to electric potential energy of two point charges and use EP

31. Physical Quantities and Units

31.1 Physical Quantities

31.1.1 Physical quantities consist of magnitude and unit

31.1.2 Estimate physical quantities from the syllabus

31.2 SI Units

31.2.1 SI base units: mass, length, time, current, temperature

31.2.2 Express derived units from SI base units

31.2.3 Check homogeneity of physical equations

31.2.4 Use prefixes (pico, nano, micro, kilo, etc.)

31.3 Errors and Uncertainties

31.3.1 Understand systematic and random errors

31.3.2 Assess uncertainty in derived quantities

31.4 uniform Electric Fields

31.4.1 Distinguish between precision and accuracy

31.5 Scalars and Vectors

31.5.1 Difference between scalar and vector quantities

31.5.2 Add and subtract coplanar vectors

31.5.3 Represent a vector as components

32. Motion in a Circle

32.1 Centripetal Acceleration

32.1.1 Understand centripetal acceleration and its role in circular motion

32.1.2 Recall and use a = rω² and a = v² / r

32.1.3 Recall and use F = mrω² and F = mv² / r

32.1.4 Understand force causing centripetal acceleration is always perpendicular to motion

32.2 Kinematics of Uniform Circular Motion

32.2.1 Recall and use ω = 2π / T and v = rω

32.2.2 Understand and use angular speed

32.2.3 Define and express angular displacement in radians

Get PDF

PDF

Explore

Your Flashcards are Ready!

Solve Problems of Uniformly Accelerated Motion

Introduction