Question

A car of mass $m$ starts moving so that its velocity varies according to the law $v=\beta \sqrt{s}$, where $\beta$ is a constant, and $s$ is the distance covered. The total work performed by all the forces which are acting on the car during the first $t$ seconds after the beginning of motion is:

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

Answer 1

The correct option is A ${m\beta }^4{t}^2/8$

$v=\beta \sqrt{s}$

$\frac{ds}{dt}=\beta \sqrt{s}$

On integration

$2\sqrt{s}=\beta t$

$s=\frac{{\beta }^2{t}^2}{4}$

$v=\frac{{\beta }^{2}t}{2}$

On differentiation with respect to t

$a=\frac{{\beta }^2}{2}$

Work =F.s=mas=$\frac{m{\beta }^4{t}^2}{8}$