Question

Work done in time l on a body of mass n which is accelerated from rest to a aspeed v in time $t_1$ as a function of time t is given by:

• A. $\frac{1}{2}\left(m\frac{v}{t_1}\right)t^2$
• B. $m\left(m\frac{v}{t_1}\right)t^2$
• C. $\frac{1}{2}{\left(\frac{mv}{t_1}\right)}^2{t}^2$
• D. $\frac{1}{2}m{v}^2{\left(\frac{t}{t_1}\right)}^2$

Answer 1

The correct option is D $\frac{1}{2}m{v}^2{\left(\frac{t}{t_1}\right)}^2$

Acceleration is a constant given by:
$a=\frac{v-0}{t_1}$
Force acting on it = ma $=\frac{mv}{t_1}$
displacement is given by:
$s=\frac{1}{2}a{t}^2$
$s=\frac{1}{2}\frac{v}{t_1}{t}^2$
i.e
Work done $=F.s=\frac{1}{2}m{v}^2(\frac{t}{t_1}{)}^2$
Option D is correct.