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 energy of the vehicle at time t is E and power developed by the motor is P, which of the following graphs are correct?
 

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,

$\mathrm{KE}=\frac{1}{2}{\mathrm{mv}}^2=\frac{1}{2}{\mathrm{ma}}^2{\mathrm{t}}^2$

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 

$\mathrm{P}=\mathrm{Fv}=\text{ Fat }$

Hence, the graph between power and time will be a straight line passing through the origin. Hence, option (a) is also correct.