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 :

Question

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 : (A) (mv2/T2)t (B) (mv2/T2)t2 (C)  (1/2) (mv2/T2)t (D)  (1/2) (mv2/T2)t2

Tardigrade Admin · Accepted Answer

F=ma=(mv/T) (∴ a=(v-0/T)) Instantaneous power= Fv =mav =(mv/T)⋅ at=(mv/T)⋅(v/T)⋅ t =(mv2/T2)t

Q. 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 :

$\frac{m v ^{2}}{T ^{2}} t$

$\frac{m v ^{2}}{T ^{2}} t^{2}$

$\frac{1}{2} \frac{m v ^{2}}{T ^{2}} t$

$\frac{1}{2} \frac{m v ^{2}}{T ^{2}} t^{2}$

$F = ma = \frac{m v}{T} (∴ a = \frac{v - 0}{T})$
Instantaneous power $= F v$
$= ma v$
$= \frac{m v}{T} \cdot a t = \frac{m v}{T} \cdot \frac{v}{T} \cdot t$
$= \frac{m v ^{2}}{T ^{2}} t$

Q. 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 :

T2mv2​t

T2mv2​t2

21​T2mv2​t

21​T2mv2​t2