First slide

Kinetic energy

Question

A ball is projected vertically upwards with an initial velocity. Which of the following graphs [Fig. (3)] best represents the K.E. of the ball as a function of time from the instant of projection till it reaches back the point of projection ?

Moderate

A
B
C
D

Solution

$, Kinetic energy at time t = 0 is given by {(K.E.)}_{t = 0} = \frac{1}{2} {mv}_{0}^{2} Kinetic energy at time t = t is given by (K . E .) t = t = \frac{1}{2} {mv}_{t}^{2} = \frac{1}{2} m {(v_{0} - gt)}^{2} (∵ v_{t} = v_{0} - gt) = \frac{1}{2} m [v_{0}^{2} + g^{2} t^{2} - 2 v_{0} gt] Equation of parabola .$

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