A small steel ball is projected vertically downward from the roof of a building 60m high with an initial speed of 5ms−1. A student chooses the upward direction as positive for analysis.
Answer the following.
(i) Write the expressions for (a) velocity v and (b) displacement s of the ball as functions of time t using the chosen sign convention.
(ii) Using the expression for displacement, determine the time taken by the ball to reach the ground.
(iii) Using the velocity–time relation, calculate the algebraic area under the v–t graph from t=0 until the instant of impact, and show that this area equals the displacement obtained in part (ii). Explain why the numerical value of this area is negative.
(iv) Draw a neat velocity–time graph for the motion in your answer book and clearly mark the physical significance of the negative area under the curve.