First slide

Power

Question

A car of mass m is accelerating on a level smooth road under the action of a single force F. The power
delivered to the car is constant and equal to P. If the velocity of the car at an instant is v, then after travelling how much distance will it become double?

Moderate

A

$\frac{7 m v^{3}}{3 P}$
B

$\frac{4 m v^{3}}{3 P}$
C

$\frac{m v^{3}}{P}$
D

$\frac{18 m v^{3}}{7 P}$

Solution

Power $P = F \cdot v = m (v \cdot \frac{d v}{d s}) \cdot v$
$∴ \int_{v}^{2 v} v^{2} \cdot d v = \frac{P}{m} \cdot \int_{0}^{s} d s$
${[\frac{v^{3}}{3}]}_{v}^{2 v} = \frac{P s}{m} or s = \frac{7 m v^{3}}{3 P}$

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