A vehicle is driven along a straight horizontal track by a motor which exerts a constant driving force. The vehicle starts from rest at `t=0` and the effects of friction and air resistance are negligible. If the kinetic eneryg of the vehicle at time t is E and power developed by the motor is P, which of the following graphs are correct?

Options

A. (a)
B. (b)
C. (c)
D. (d)

Answer

A, C

Explanation

Since, force on the vehicle is constant, it will move with a constant acceleration.
Let this acceleration be a.
Then at time t, its velocity will be equal to `v=at`.
Hence, at time t, the kinetic energy,
`KE=1/2mv^2=1/2ma^2t^2`
It means, graph between E and t will be a parabola of increasing slope. Hence, option (c) is correct.
The power associated with the force is equal to
`P=Fv=Fat`.
Hence, the graph between power and time will be a straight line passing through the origin. Hence, option (a) is also correct.