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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a
vot+13bt2
b
vot+13bt3
c
vot+16bt3
d
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
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