Question

A body starts from rest acquires a velocity $v$ in time $T$. The work done on the body in time$t$ will be proportional to

• A. $\left(\frac{V^2}{T^2}\right)t^2$
• B. $\left(\frac{V^2}{T^2}\right)t$
• C. $\left(\frac{V^2}{T^{}}\right)t^2$
• D. $\left(\frac{V^{}}{T^{}}\right)t^2$

Answer 1

Answer: (A)

$\left(\frac{V^2}{T^2}\right)t^2$

The acceleration of the body $a=\frac{v}{T}$
Now, work done $=\frac{1}{2}m{v}^2\propto v^2$
Here $v=u+at$
so, work done $v^2\propto a^2{t}^2$
or $W\propto \left(\frac{v^2}{T^2}\right)t^2$