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

$ \frac{1}{2} mV ^2= Pt $
$ V =\sqrt{\frac{2 Pt }{ m }} $
$ \frac{ dx }{ dt }=\sqrt{\frac{2 Pt }{ m }} $
$ x =\sqrt{\frac{2 P }{ 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$