Question

A car of mas sm starts moving so that its velocity varies according to the law $v=\beta \sqrt{s}$ where $\beta$ is a constant, ands 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 $m{\beta }^4{t}^2/8$

$v^2=u^2+2as$
${\beta }^{2}s=0+2as$
$a=\frac{{\beta }^2}{2}$
$s=ut+0.5a{t}^2$
$s=0+0.5\left({\beta }^2/2\right)t^2$
Work=mas
W=$m\left({\beta }^2/2\right)\left(0.5\right({\beta }^2/2\left)t^2\right)$
W=$\frac{m{\beta }^4{t}^2}{8}$