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Question

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


A

t12

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B

t34

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C

t32

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D

t2

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Solution

The correct option is C

t32


We know that, Power,
P=Fv=mdvdt.vvdv=Pmdt
Integrating both sides, we have
vdv=Pmdt ( P = constant)
v22=Ptm
v=2Pmt12
dxdt=2Pmt12
dx=2Pmt12dt
Integrating again, we have
dx=2Pmt12dt
x=232Pmt32
xt32.
Hence, the correct choice is (c).


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