Q. 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 car is proportional to
A) t²P₀
B) t^(1/2)
C) t^(−1/2)
D) t/√m
Explanation
[Solution from source] With constant power, the work done equals the kinetic energy gained: P₀t = ½mv², so v = √(2P₀t/m) and v ∝ t^(1/2). The velocity grows ever more slowly, not linearly or as t². Answer (2).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.