A body is moved along a straight line by a machine delivering a power proportional to time ( $P \propto t$ ). Then:

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Solution

Power is the rate of doing work and we can write it mathematically as,
$P = \frac{d W}{d t} = k t$
$\int P d t = W = k_{1} t^{2} = K E = 0.5 m v^{2}$
$∴ W o r k - d o n e i s p r o p o r t i o n a l t o t^{2}$
Velocity is given by,
$v = k_{2} t$
$V e l o c i t y i s p r o p o r t i o n a l t o t$
displacement is given by,
$s = \int v d t = k_{0} t^{2}$
$D i s p l a c e m e n t i s P r o p o r t i o n a l t o t^{2}$

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