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Question

The displacement x of a particle moving in one dimension under the action of a constant force is related to time t by the equation t3=x where x is in metres and t is in seconds. Find the displacement of the particle when its velocity is zero.

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Solution

Given t3=xx=t3x=(t3)2=t26t+9
Therefore, the velocity of the particle is
v=dxdt=2t6
and it will be zero when
2t6=0t=3s
Hence, the velocity of the particle will be zero when t = 3 s. Putting t = 3 s. in (1), we get the required displacement of the particle as
x=326×3+9=0
x=0

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