Question

A car drives along straight level frictionless road by an engine delivering constant power. Then velocity is directly proportional to ?

• A. t
• B. $\frac{1}{\sqrt{t}}$
• C. $\sqrt{t}$
• D. None of these

Answer 1

Answer: (C)

$\sqrt{t}$

Power, $P=F.V$

$\Rightarrow P=$ Constant

$\Rightarrow P=maV$

$=m\frac{dv}{dt}.V$

$\Rightarrow Pdt=mvdv$

Integrating both sides,

$\Rightarrow \int Pdt=\int mvdv$

$\Rightarrow Pt=\frac{m{V}^2}{2}$

$V\propto \sqrt{t}.$

Hence, the answer is $\sqrt{t}.$