A car of mass m starts from rest and accelerates so that the instantaneo...

A car of mass m starts from rest and accelerates so that the instantaneous power delivered to the car has a constant magnitude P0. The instantaneous velocity of this cat is proportional to (a) t2P0 (b) t1/2 (c) t-1/2 (d) t/√m 

AIPMT/NEET 2012 | W.P.E Q 4 | Instantaneous power is given constant so dot product of force and velocity is constant. Body is acceleration from rest so angle between force and velocity is zero because this force only is the cause of its motion. From Newton’s second law , we know the relation between force and acceleration. Acceleration will come in terms of force and mass and later on in terms of force mass and instantaneous velocity. From equation of motion we have another relation between instantaneous velocity and acceleration so finally we will get the desired result. In a single qus we have application of W.P.E , Newton’s laws of motion and Kinematics so obviously it may not be an easy qus for many students.

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