Question

A locomotive of mass $m$ has a velocity $v=a\sqrt{x}$. Find the work done by all the forces acting on locomotive in first $t$ sec.

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

Answer 1

Answer: (C)

$\frac{m{a}^4{t}^2}{8}$

$\frac{dv}{dt}=\frac{dv}{dx}\cdot \frac{dx}{dt}=\frac{a}{2\sqrt{x}}\left(a\sqrt{x}\right)h=\frac{a^2}{2}$
$\therefore F=\frac{m{a}^2}{2}$
$S=ut+\frac{1}{2}F{t}^2=0+\frac{a^2}{4}{t}^2$
$W=F.s=\frac{m{a}^4{t}^2}{8}$