Question

Work done in time $t$ on a body of mass $m$ which is accelerated from rest to speed $v$ in time $t_1$ as a function of time $t$ is given as

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

Answer 1

The correct option is A $\frac{1}{2}m\frac{v^2}{t_1^2}{t}^2$

Work done $=Force\times displacement$
$F=ma$
and $s=\frac{1}{2}a{t}^2$
Using, $s=ut+\frac{1}{2}a{t}^2)$
$\therefore W=ma\times \frac{1}{2}a{t}^2$
$=\frac{1}{2}m{a}^2{t}^2$
$=\frac{1}{2}m{\left(\frac{v}{t_1}\right)}^2{t}^2[usinga=\frac{v}{t_1}]$
$=\frac{1}{2}m\frac{v^2}{t_1^2}{t}^2$.