question_answer

A body of mass m is accelerated uniformly from rest to a speed v in a time T. The instantaneous power delivered to the body as a function of time, is given by                               [AIEEE 2005]

A) \[\frac{m{{v}^{2}}}{{{T}^{2}}}t\]

B) \[\frac{m{{v}^{2}}}{{{T}^{2}}}{{t}^{2}}\]

C) \[\frac{1}{2}\frac{m{{v}^{2}}}{{{T}^{2}}}{{t}^{2}}\]

D) \[\frac{1}{2}\frac{m{{v}^{2}}}{{{T}^{2}}}{{t}^{2}}\]

Correct Answer: A

Solution :

[a] The force

Instantaneous power

(force F and velocity v both are in same direction)

Instantaneous process delivered in time t

(from equation of motion,)