First slide

Power

Question

A body is moved along a straight line by a machine delivering a constant power. The distance moved by the body in time ‘t’ is proportional to

Easy

A

$t^{1 / 2}$
B

$t^{3 / 4}$
C

$t^{3 / 2}$
D

$t^{1 / 4}$

Solution

$P = Fv = mav = m (\frac{dv}{dt}) v \Rightarrow \frac{P}{m} dt = vdv$
$\Rightarrow \frac{P}{m} \times t = \frac{v^{2}}{2} \Rightarrow v = {(\frac{2 P}{m})}^{1 / 2} (t)^{1 / 2} now$
$s = \int vdt = \int {(\frac{2 P}{m})}^{1 / 2} t^{1 / 2} dt$
$∴ s = {(\frac{2 P}{m})}^{1 / 2} [\frac{2 t^{3 / 2}}{3}] \Rightarrow s \propto t^{3 / 2}$

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