Question

The velocity ${}^{\prime }{v}^{\prime }$ reached by a car of mass ${}^{\prime }{m}^{\prime }$ at certain distance from the starting point driven with constant power ${}^{\prime }{P}^{\prime }$ is such that:

• A. $v\propto \frac{3P}{m}$
• B. $v^2\propto \frac{3P}{m}$
• C. $v^3\propto \frac{3P}{m}$
• D. $v\propto {\left(\frac{3P}{m}\right)}^2$

Answer 1

The correct option is C $v^3\propto \frac{3P}{m}$

Power of car=$F.v=mav=P$

$⟹a=\frac{P}{mv}=\frac{vdv}{ds}$

$⟹{\int }_0^v{v}^{2}dv={\int }_0^s\frac{P}{m}ds$

$⟹\frac{v^3}{3}=\frac{Ps}{m}$

$⟹v^3\propto \frac{3P}{m}$