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 ) :
Option: 1
Option: 2
Option: 3
Option: 4

Answers (1)

\begin{array}{l} \frac{\mathrm{dK}}{\mathrm{dt}}=\mathrm{P}=\operatorname{costant} \\\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}}\\ \\ \Rightarrow \mathrm{S}=\sqrt{\frac{2 \mathrm{P}}{\mathrm{m}}} *\frac{2}{3}* \mathrm{t}^{\frac{3}{2}} \end{array}

i.e s \ \alpha \ \mathrm{t}^{\frac{3}{2}}

So the correct graph is

 

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