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,KE=12mv2=12ma2t2It 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.