(ii) A force F acts on a body of mass m, causing the body to accelerate at a ms-2. The body travels through a distance s m in time t s in the direction of the force. Show that the work done is equal to change in the kinetic energy of the body.

To show that the work done is equal to the change in kinetic energy, we can use the work-energy principle. Step 1: Work Done by Force The work done \( W \) by a force \( F \) is given by: W = F · s Step 2: Force and Acceleration From Newton's second law, the force \( F \) is: F = m · a Substitute this into the work done equation: W = m · a · s Step 3: Kinematic Equation Using the kinematic equation: v^2 = u^2 + 2as where \( v \) is the final velocity and \( u \) is the initial velocity. Rearrange to find \( as \): as = (v^2 - u^2)/(2) Step 4: Substitute into Work Done Substitute \( as \) into the work done equation: W = m · (v^2 - u^2)/(2) Step 5: Change in Kinetic Energy The change in kinetic energy \( KE\) is: KE = (1)/(2) m v^2 - (1)/(2) m u^2 Step 6: Equate Work Done and Change in Kinetic Energy Thus, the work done is equal to the change in kinetic energy: W = KE Conclusion: The work done by the force is equal to the change in kinetic energy of the body. Final Answer: W = KE