A student is investigating the speed of a vehicle on a track when a small ball is projected into the vehicle, as shown in Fig. 1.1. ball vehicle track [Figure 1.1] The ball is projected towards the vehicle by a compressed spring. It is suggested that the relationship between the speed v of the vehicle and its mass M, after the ball embeds itself in the vehicle, is kx² = (M + b)v² where b is the mass of the ball, k is the spring constant and x is the compression of the spring. Design a laboratory experiment to test the relationship between v and M. Explain how your results could be used to plot a graph with 1/v² on the y-axis and to determine a value for k. You should draw a diagram, on page 3, showing the arrangement of your equipment. In your account you should pay particular attention to • the procedure to be followed • the measurements to be taken • the control of variables • the analysis of the data • any safety precautions to be taken.