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 v3The relation between time t and displacement x is given byt=αx2+βx. . .. . .. . . .(1)Differentiate above equation with respect to x,dtdx=2αx+βand we know that velocity, v=dxdtv=12αx+β. . . . . .(2)acceleration, a=dvdta=−1(2αx+β)22αdxdta=−2αv3 (by putting equation 2)The acceleration of the particle is directly proportional to the cubic of velocity.a∝v3The correct option is A.

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