First slide

Power

Question

A body is moving under the expense of a constant power. If 'X' is the displacement in time 't', then 'x' is proportional to

Moderate

A

$t^{\frac{2}{3}}$
B

$t^{\frac{3}{2}}$
C

$t^{2}$
D

$t^{\frac{1}{2}}$

Solution

$P = F v = m \frac{d v}{d t} v \Rightarrow v d v = \frac{P}{m} d t$

$\int v d v = \int \frac{P}{m} d t \Rightarrow v = \sqrt{\frac{2 P t}{m}}$
$\frac{d s}{d t} = \sqrt{\frac{2 P t}{m}} o r, d s = \sqrt{\frac{2 P t}{m}} d t s = \int_{0}^{t} \sqrt{\frac{2 P t}{m}} d t$
$s \infty t^{\frac{3}{} 2}$

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