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(a) (i) Define velocity. [1]
(ii) Distinguish between speed and velocity. [2]
(b) A car of mass 1500 kg moves along a straight, horizontal road.
The variation with time $t$ of the velocity $v$ for the car is shown in Fig. 1.1.
The brakes of the car are applied from $t = 1.0$ s to $t = 3.5$ s.
For the time when the brakes are applied,
(i) calculate the distance moved by the car, [3]
(ii) calculate the magnitude of the resultant force on the car. [3]
(c) The direction of motion of the car in (b) at time $t = 2.0$ s is shown in Fig. 1.2.
On Fig. 1.2, show with arrows the directions of the acceleration (label this arrow A) and the resultant force (label this arrow F). [1]
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(a) (i) Define power. [1]
(ii) Use your definition in (i) to show that power may also be expressed as the product of
force and velocity. [2]
(b) A lorry moves up a road that is inclined at 9.0° to the horizontal, as shown in Fig. 2.1.
The lorry has mass 2500 kg and is travelling at a constant speed of 8.5 ms−1. The force due to
air resistance is negligible.
(i) Calculate the useful power from the engine to move the lorry up the road. [3]
(ii) State two reasons why the rate of change of potential energy of the lorry is equal to the
power calculated in (i). [2]
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A uniform plank AB of length 5.0 m and weight 200 N is placed across a stream, as shown in figure 1.
A man of weight 880 N stands a distance x from end A. The ground exerts a vertical force $F_A$ on the plank at end A and a vertical force $F_B$ on the plank at end B. As the man moves along the plank, the plank is always in equilibrium.
(a) (i) Explain why the sum of the forces $F_A$ and $F_B$ is constant no matter where the man stands on the plank. [2]
(ii) The man stands a distance $x = 0.50 , ext{m}$ from end A. Use the principle of moments to calculate the magnitude of $F_B$. [4]
(b) The variation with distance x of force $F_A$ is shown in Figure 2.
On the axes of Fig. 3.2, sketch a graph to show the variation with x of force $F_B$. [3]
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A metal ball of mass 40g falls vertically onto a spring, as shown in Fig. 4.1.
The spring is supported and stands vertically. The ball has a speed of 2.8ms$^{-1}$ as it makes contact with the spring. The ball is brought to rest as the spring is compressed.
(a) Show that the kinetic energy of the ball as it makes contact with the spring is 0.16J. [2]
(b) The variation of the force $F$ acting on the spring with the compression $x$ of the spring is shown in Fig. 4.2.
The ball produces a maximum compression $X_B$ when it comes to rest. The spring has a spring constant of 800 N m$^{-1}$. Use Fig. 4.2 to
(i) calculate the compression $X_B$, [2]
(ii) show that not all the kinetic energy in (a) is converted into elastic potential energy in the spring. [2]
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(a) Explain what is meant by the following quantities for a wave on the surface of water:
(i) displacement and amplitude, [2]
(ii) frequency and time period. [2]
(b) Fig. 5.1 represents waves on the surface of water in a ripple tank at one particular instant of time.
A vibrator moves the surface of the water to produce the waves of frequency \( f \). The speed of the waves is \( 7.5\, \text{cm s}^{-1} \). Where the waves travel on the water surface, the maximum depth of the water is \( 15\, \text{mm} \) and the minimum depth is \( 12\, \text{mm} \).
(i) Calculate, for the waves,
- the amplitude, [1]
- the wavelength. [2]
(ii) Calculate the time period of the oscillations of the vibrator. [2]
(c) State and explain whether the waves on the surface of the water shown in Fig. 5.1 are
(i) progressive or stationary, [1]
(ii) transverse or longitudinal. [1]
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(a) Distinguish between electromotive force (e.m.f.) and potential difference (p.d.).
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(b) A battery of e.m.f. 12V and internal resistance 0.50Ω is connected to two identical lamps, as shown in Fig. 6.1.
[Image_1: Fig. 6.1]
Each lamp has constant resistance. The power rating of each lamp is 48W when connected across a p.d. of 12V.
(i) Explain why the power dissipated in each lamp is not 48W when connected as shown in Fig. 6.1.
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(ii) Calculate the resistance of one lamp.
resistance = ........................................................ Ω
(iii) Calculate the current in the battery.
current = ........................................................... A
(iv) Calculate the power dissipated in one lamp.
power = ............................................................. W
(c) A third identical lamp is placed in parallel with the battery in the circuit of Fig. 6.1. Describe and explain the effect on the terminal p.d. of the battery.
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(a) State what is meant by
$\alpha$-particle: ............................................................................................................................................
$\beta$-particle: ...................................................................................................................................................
$\gamma$-radiation: .......................................................................................................................................... [2]
(b) Describe the changes to the proton number and the nucleon number of a nucleus when emission occurs of
(i) an $\alpha$-particle,
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.............................................................................................................................................................. [1]
(ii) a $\beta$-particle,
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(iii) $\gamma$-radiation.
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.............................................................................................................................................................. [1]
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