First slide

Power

Question

A body is moved along a straight line by a machine delivering constant power. The distance moved by the body in time t is proportional to

Moderate

A

$t^{1 / 2}$
B

$t^{3 / 4}$
C

$t^{3 / 2}$
D

t²

Solution

$v \times (m \frac{d v}{d t}) = P I n t e g r a t i n g, v = \frac{2 P t}{m} \Rightarrow \frac{d s}{d t} = \frac{2 P t}{m} \Rightarrow d s = \frac{2 P}{m} t d t \Rightarrow \int_{0}^{s} d s = \frac{2 P}{m} \int_{0}^{t} t d t \Rightarrow s \infty t^{\frac{3}{2}}$

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