Question

A locomotive of mass $m$ starts moving with velocity $v=\alpha \sqrt{s}$ where $\alpha$ is constant $s$ is distance traversed. The total work done by all the forces acting on the locomotive during first $t$ sec.

• A. $\frac{1}{2}m{\alpha }^4{t}^2$
• B. $\frac{1}{4}m{\alpha }^4{t}^2$
• C. $\frac{1}{8}m{\alpha }^4{t}^2$
• D. $\frac{1}{16}m{\alpha }^4{t}^2$

Answer 1

The correct option is C $\frac{1}{8}m{\alpha }^4{t}^2$

A locomotive of mass $=m$

Velocity $v=\alpha \sqrt{s}$

$\alpha =$ constant

$s=$ distance transversed

Total work done by all the forces acting on the locomotive during first

$=tsec$

Work done$=$ Force $\times$ displacement

$=mass\times acceleration\times Displacement=m\times \frac{a^2}{2}\times (\frac{at}{2}{)}^2=m\times \frac{a^2}{2}\times \frac{a^2{t}^2}{4}=\frac{1}{8}{a}^{4}m{t}^2$