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Question

A particle at rest is moved along a straight line by a machine giving constant power. The distance moved by the particle in time t is proportional to

A
t1/2
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B
t2/3
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C
t
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D
t3/2
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Solution

The correct option is D t3/2
Power, P= Force × Velocity
=F×v
=ma×v= constant
So, va= constant
vdvdt= constant
Integrating it, we have
v22=Ct
or v=2Ct=C1t1/2
or dxdt=C1t1/2
Integrating it, we get
x=C2t3/2
So, xt3/2

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