Fig. below shows the motion of a train over a section of track which includes a sharp bend.

(a) The section of the track with the sharp bend has a maximum speed restriction. The train decelerates approaching the bend so that at the start of the bend it has just reached the maximum speed allowed. The train is driven around the bend at the maximum speed allowed and accelerates immediately on leaving the bend.

(i) What is the maximum speed allowed round the bend in the track?

(ii) How long does the train take to travel the bend of the track?

(iii) Calculate the length of the bend.

(b) The train has to slow down to go around the bend. Calculate the deceleration.

(c) As the train is driven round the bend, what is the name of the extra force acting?

(i) Draw an arrow to show the direction of this force.

(ii) State the effect that this force has on the motion.

(iii) State how this force is provided.

Fig. below shows the speed-time graph for a bus during tests.

At time t = 0, the driver starts to brake.

(a) For test 1,

(i) determine how long the bus takes to stop,

(ii) state which part of the graph shows the greatest deceleration,

(iii) use the graph to determine how far the bus travels in the first 2 seconds.

(b) For test 2, a device was fitted to the bus. The device changed the deceleration.

(i) State two ways in which the deceleration during test 2 is different from that during test 1.

(ii) Calculate the value of the deceleration in test 2.

(a) A stone falls from the top of a building and hits the ground at a speed of 32 m/s.

The air resistance-force on the stone is very small and may be neglected.

(i) Calculate the time of fall.

(ii) On Fig. below, draw the speed-time graph for the falling stone.

(iii) The weight of the stone is 24 N.

Calculate the mass of the stone.

(b) A student used a suitable measuring cylinder and a spring balance to find the density of a sample of the stone.

(i) Describe how the measuring cylinder is used, and state the readings that are taken.

(ii) Describe how the spring balance is used, and state the reading that is taken.

(iii) Write down an equation from which the density of the stone is calculated.

(iv) The student then wishes to find the density of cork. Suggest how the apparatus and the method would need to be changed.

A small rubber ball falls vertically, hits the ground and rebounds vertically upwards. Fig. below is the speed-time graph for the ball.

(a) Using information from the graph, describe the following parts of the motion of the ball.

(i) part AB

(ii) part DE

(b) Explain what is happening to the ball along the part of the graph from B through C to D.

(c) Whilst the ball is in contact with the ground, what is the

(i) overall change in speed,

(ii) overall change in velocity?

(d) Use your answer to (c) to explain the difference between speed and velocity.

(e) Use the graph to calculate the distance travelled by the ball between D and E.

(f) Use the graph to calculate the deceleration of the ball between D and E.

Fig. below shows a cycle track.

A cyclist starts at A and follows the path ABCDEB.

The speed-time graph is shown below.

(a) Use information from Fig. 1.1 and Fig. 1.2 to describe the motion of the cyclist

(i) along AB,

(ii) along BCDEB.

(b) The velocity v of the cyclist at C is shown in Figure.

State one similarity and one difference between the velocity at C and the velocity at E.

similarity

difference

(c) Calculate

(i) the distance along the cycle track from A to B,

(ii) the circumference of the circular part of the track.

A solid plastic sphere falls towards the Earth.

Fig. below is the speed-time graph of the fall up to the point where the sphere hits the Earth’s surface.

(a) Describe in detail the motion of the sphere shown by the graph.

(b) Draw arrows to show the directions of the forces acting on the sphere when it is at the position shown by point S on the graph. Label your arrows with the names of the forces.

(c) Explain why the sphere is moving with constant speed at S.

(d) Use the graph to calculate the approximate distance that the sphere falls

(i) between R and T,

(ii) between P and Q.