Question

A body of mass $2\, kg$ is initially at rest It starts moving unidirectionally under the influence of a source of constant power P Its displacement in $4 s$ is $\frac{1}{3} \alpha^2 \sqrt{P} m$ The value of $\alpha$ will be_______

Answer 1

Correct Answer: 4

The correct answer is 4.
$\frac{1}{2}m{V}^2=Pt$
$V=\sqrt{\frac{2Pt}{m}}$
$\frac{dx}{dt}=\sqrt{\frac{2Pt}{m}}$
$x=\sqrt{\frac{2P}{m}\frac{2}{3}}{\left[t^{3/2}\right]}_0^4$
$x=\frac{16\sqrt{P}}{3}=\frac{1}{3}\times 16\sqrt{P}$
$\alpha =4$