The work done in time ‘t’ on a body of mass ‘m’ which is accelerated from rest to a speed ‘v’ in time $' t_{1}'$ as a function of time ‘t’ is given by

see full answer

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

\frac{1}{2} \frac{{mv}^{2}}{t_{1}^{2}} t^{2}

\frac{1}{2} {(\frac{mv}{t_{1}})}^{2} t^{2}

\frac{mv}{t_{1}} t^{2}

\frac{1}{2} m \frac{v}{t_{1}} t^{2}

answer is D.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

given that

A body of mass m at rest is accelerated for $t_{1}$ seconds

Until its final velocity is v

Acceleration $= \frac{v - 0}{t_{1}}$

$a = \frac{v}{t_{1}}$

Force applied $F = m a$

$\Rightarrow F = \frac{m v}{t_{1}}$

Displacement produced ‘s’ is expressed as function of time t

$s = u t + \frac{1}{2} a t^{2}$ $∵ u = 0, a = \frac{v}{t_{1}}$

$s = \frac{1}{2} \frac{v}{t_{1}} t^{2}$

Hence work done $W = F \times S$

$W = \frac{m v}{t_{1}} \times \frac{1}{2} \frac{v}{t_{1}} t^{2}$

So correct option is (d).

Watch 3-min video & get full concept clarity