A body at rest is moved along a horizontal straight line by a machine delivering a constant power. d

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5.Work, Energy, Power and Collision

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A body at rest is moved along a horizontal straight line by a machine delivering a constant power. The distance moved by the body in time $t^{\prime}$ is proportional to :

A

$t^{\frac{1}{4}}$

B

$t^{\frac{3}{4}}$

C

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

D

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

Solution

${P}=$ constant

$\frac{1}{2} m v^{2}=P_{t}$ $\Rightarrow v \propto \sqrt{t}$

$\frac{d x}{d t}=C \sqrt{t} \quad c=$ constant

$\frac{1}{2} m v^{2}=P_{t}$

$\Rightarrow v \propto \sqrt{t}$

by integration.

$x =C \frac{t^{\frac{1}{2}+1}}{\frac{1}{2}+1}$

$x\propto t^{3 / 2}$

Standard 11

Physics

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