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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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wkt, a=change in velocitychange in time=dvdt

∴dvdt=bt now integrating this we will get v

v=bt22+c

At t=0 s, v=v0, Thus v0=c

∴v=bt22+v0

Now. v=change in positionchange in time=dsdt=bt22+v0

∴ds=(bt22+v0)dt

∴ Integrating the above we get, s=bt36+v0t+c′at t=0, s=0∴c′=0

i.e. s=bt36+v0t

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