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 it becomes 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

P= Fv = constant
$\begin{array}{l} ∴ F = \frac{P}{v} \Rightarrow m a = \frac{P}{v} \\ \Rightarrow ∴ m (\frac{d v}{d s}) (\frac{d s}{d t}) = \frac{P}{v} \sin c e a c c e l e r a t i o n = \frac{d v}{d t} = \frac{d v}{d s} \frac{d s}{d t} a n d \frac{d s}{d t} = v \\ \frac{m}{P} \int_{v}^{2 v} v^{2} d v {= \int}_{0}^{s} d S \\ \frac{m}{P} {[\frac{v^{3}}{3}]}^{2 v}_{v} = S \\ \frac{7 m v^{3}}{3 P} = S \end{array}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App