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Question

The relation between time t and displacement x is t=αx2+βx where α and β are constants then acceleration of particle is proportional to-

A
v3
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B
v2
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C
v3/2
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D
v2/3
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Solution

The correct option is A v3
The relation between time t and displacement x is given by
t=αx2+βx. . .. . .. . . .(1)
Differentiate above equation with respect to x,
dtdx=2αx+β
and we know that
velocity, v=dxdt
v=12αx+β. . . . . .(2)
acceleration, a=dvdt
a=1(2αx+β)22αdxdt
a=2αv3 (by putting equation 2)
The acceleration of the particle is directly proportional to the cubic of velocity.
av3
The correct option is A.

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