A resultant force F moves an object of mass m through distance s in a straight line. The force gives the object an acceleration a so that its speed changes from initial speed u to final speed v.

1. (a)(i)1.the work W done by the force, in terms of a, m and s W = ..................................................................................... [1][1]
2. (a)(i)2.the distance s, in terms of a, u and v. s = ..................................................................................... [1][1]
3. (a)(ii)Use your answers in (i) to show that the kinetic energy of the object is given by kinetic energy = ½ × mass × (speed)². Explain your working. [2][2]
4. (b)A ball of mass 0.040 kg is projected into the air from horizontal ground, as illustrated in Fig. 2.1. [Figure 2.1]
5. (b)(i)For the movement of the ball from X to Y, draw a solid line on Fig. 2.1 to show: 1. the distance moved (label this line D) 2. the displacement (label this line S). [2][2]
6. (b)(ii)By consideration of energy transfer, determine the height h of point Y above the ground. h = ..................................................................... m [3][3]
7. (b)(iii)On Fig. 2.2, sketch the variation of the kinetic energy of the ball with its vertical height above the ground for the movement of the ball from X to Y. Numerical values are not required. [Figure 2.2] [2][2]

This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.