An object moves along a straight line, goes to a certain point, and returns to its starting point in a total time of t seconds. Read the instructions carefully and answer in the order given.
(i) Starting only from the definitions of distance and displacement, prove that the average velocity of any object that returns to its starting point is zero, whereas its average speed need not be zero.
(ii) A ball is thrown vertically upward with an initial speed of 20m/s and is caught at the thrower’s hand at the same height. Taking upward as positive and g=10m/s2 (downward), calculate:
(a) the total time of flight,
(b) the total distance travelled by the ball,
(c) the displacement of the ball at the instant it is caught,
(d) the average speed and the average velocity for the whole motion.
(iii) Explain how the numerical results of part (ii) illustrate the general proof obtained in part (i).