Question

Work done in time $t$ on a body of mass $m$ which is accelerated from rest to a speed $v$ in time 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. $\frac{1}{2}m{\left(\frac{v}{t_1}\right)}^2{t}^2$
• D. $\frac{1}{2}m\frac{v}{t_1^2}{t}^2$

Answer 1

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

Ans : We know $W=F\times s$

where,

$F=ma$

By using Kinematics, $s=\frac{1}{2}a{t}^2$ , if u =0

So,

$W=\left(ma\right).\left(\frac{1}{2}a{t}^2\right)$

$W=\frac{1}{2}m{a}^2{t}^2$ where $a=v/t_1$

$W=\frac{1}{2}m(\frac{v}{t_1}{)}^2{t}^2$