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Question

Acceleration of a particle is increasing linearly with time t as bt. The particle starts from the origin with an initial velocity v0. The distance travelled by the particle in time t will be

A
v0t+bt36
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B
v0t+bt23
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C
v0t+bt33
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D
v0t+bt22
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Solution

The correct option is C v0t+bt33
a=btdvdt=btdv=btdt
Integrating both sides, we get
vvo=bt22v=vo+bt22dxdt=vo+bt22dx=(vo+bt22)dt
Integrating both sides, we get
Δx=vot+bt36

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