First slide

Power

Question

A body initially at rest 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^¾
C

t^{3/ 2}
D

t²

Solution

$P = Fv = (m \frac{dv}{dt}) v; m v d v = P d t \Rightarrow v^{2} \propto t \Rightarrow v \propto t^{1 / 2} \Rightarrow x \propto t^{3 / 2}$

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