JEE Main · 2005 · 08 May 2005 · Offline · Work, Power & Energy

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 time is given by

(A) $\frac{m v ^{2}}{T ^{2}} \cdot t$ ✓ Correct
(B) $\frac{m v ^{2}}{T ^{2}} \cdot t^{2}$
(C) $\frac{1}{2} \frac{m v ^{2}}{T ^{2}} \cdot t$
(D) $\frac{1}{2} \frac{mv ^{2}}{T ^{2}} \cdot t^{2}$

Answer: (A)

Solution

The uniform acceleration is

a = \frac{v}{T}

, so the speed at time

t

v (t) = a t = \frac{v}{T} t

and the force is

F = ma = \frac{m v}{T}

. The instantaneous power is

P = F v (t) = \frac{m v}{T} \cdot \frac{v}{T} t = \frac{m v ^{2}}{T ^{2}} t

JEE Main · 2005 · 08 May 2005 · Offline · Single correct option

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