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) :
Correct Option: , 3
Solution:
$\frac{\mathrm{dK}}{\mathrm{dE}}=\mathrm{P}=\cos \mathrm{t} \Rightarrow \mathrm{K}=\mathrm{Pt}=\frac{1}{2} \mathrm{mV}^{2}$
$\therefore \mathrm{V}=\sqrt{\frac{2 \mathrm{Pt}}{\mathrm{m}}}=\frac{\mathrm{ds}}{\mathrm{dt}} \therefore \mathrm{S}=\sqrt{\frac{2 \mathrm{P}}{\mathrm{m}}} \frac{2}{3} \mathrm{t}^{\frac{3}{2}}$