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The acceleration of a particle is increa...

The acceleration of a particle is increasing linerly with time t as bt. The particle starts from the origin with an initial velocity `v_(0)`. The distance travelled by the particle in time t will be

A

`v_0t+1/6bt^3`

B

`v_0t+1/3bt^3`

C

`v_0t+1/3bt^2`

D

`v_0t+1/2bt^2`

Text Solution

Verified by Experts

The correct Answer is:
A
`a=bt`
`:. (dv)/(dt)=bt`
or `int_(v_0)^vdv=int_0^t(bt)dt`
`:. v=v_0+(bt^2)/2`
`s=int_0^t vdt=int_0^t(v_0+(bt^2)/2)dt`
`=v_0t+(bt^3)/6`
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