Question 133: Work, Energy and Power & Circular Motion

Question

A particle is moving unidirectionally on a horizontal plane under the action of a constant power
supplying energy source. The displacement (s) - time (t) graph that describes the motion of the
particle is (graphs are drawn schematically and are not to scale) :

Accepted Answer

$$P = Fv$$
$$P = m{{dv} \over {dt}}v$$
$$ \Rightarrow $$ $$vdv = {P \over m}dt$$
Integrating both sides, we get
$${V^2} = k't$$
$$ \Rightarrow $$ V = k"$$\sqrt t $$
$$ \Rightarrow $$ $${{ds} \over {dt}}$$ = k"$$\sqrt t $$
$$ \Rightarrow $$ $$\int {ds}  = \int {k''\sqrt t } dt$$
$$ \Rightarrow $$ s $$ \propto $$ t
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Work, Energy and Power & Circular Motion

A particle is moving unidirectionally on a horizontal plane under the action of a constant power supplying energy source. The displacement (s) - time (t) graph that describes the motion of the particle is (graphs are drawn schematically and are not to scale) :

Choose the correct answer: