The 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

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vot+13bt2

vot+13bt3

vot+16bt3

vot+12bt2

answer is C.

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Detailed Solution

dvdt = bt ⇒dv = bt dt ⇒v = bt22+K1At t = 0, v = vo ⇒ K1= voWe get, v = 12bt2+voAgain dxdt = 12bt2+vo ⇒x = 12bt33+vot+K2At t = 0, x = 0 ⇒K2= 0∴ x = 16bt3+vot

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