Question

A car drives along smooth straight level road by an engine giving constant power. The velocity is directly proportional to

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

Answer 1

Answer: (C)

$\sqrt t$

Answer 2

P = $F \upsilon = ma \upsilon = m \frac{d \upsilon}{dt} \upsilon$ i.e. $\upsilon d \upsilon = \frac{p}{m} dt$ Integrating, we get $\frac{\upsilon^2}{2} = \frac{p}{m} t$ i.e. $\upsilon^2 \, \propto \, t$ i.e. $\upsilon \, \propto \, t^{1/2}$