Question

The speed $v$ reached by a car of mass $m \, $ driven with constant power $P$ is given by

• A. $v=\frac{3 x P}{m}$
• B. $v=\left(\frac{3 x P}{m}\right)^{1 / 2}$
• C. $v=\left(\frac{3 x P}{m}\right)^{1 / 3}$
• D. $v=\left(\frac{3 x P}{m}\right)^{2}$

Answer 1

Answer: (C)

$P=Fv$
or $P=\left(m v \frac{d v}{d x}\right)v$
or $\displaystyle \int _{0}^{v} v^{2} d v = \, \displaystyle \int _{0}^{x} \frac{P}{m} d x$
$\frac{v^{3}}{3}= \, \frac{P x}{m}$ or $v=\left(\frac{3 P x}{m}\right)^{1 / 3}$