Question

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

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

Answer 1

The correct option is D

$\frac{1}{2}m\frac{v^2}{t_1^2}{t}^2$

Work done $=F\times s=ma\times \frac{1}{2}a{t}^2$ $[froms=ut+\frac{1}{2}a{t}^2]$
$\therefore W=\frac{1}{2}m{a}^2{t}^2=\frac{1}{2}m{\left(\frac{v}{t_1}\right)}^2{t}^2$ $[Asa=\frac{v}{t_1}]$