Question 263: Work, Energy and Power & Circular Motion

Question

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

Accepted Answer

$$P = Fv$$
$$m{{vdv} \over {dt}} = P$$
$$m\int_0^v {vdv = \int_0^t {Pdt} } $$
$${{m{v^2}} \over 2} = Pt$$
$$v = \sqrt {{{2P} \over m}} {t^{1/2}}$$
$$\int_0^s {dx = \sqrt {{{2P} \over m}} \int_0^t {{t^{1/2}}dt} } $$
$$s = {2 \over 3}\sqrt {{{2P} \over m}} {t^{3/2}}$$
or $$s = {2 \over 3}\sqrt {{{2P} \over 2}}  	imes {4^{3/2}}$$
$$ = {{16} \over 3}\sqrt P ~m$$
So, $$\alpha  = 4$$

Work, Energy and Power & Circular Motion

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

Integer / Numeric Answer Type