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The acceleration of a particle is increa...

The acceleration of a particle is increasing linearly 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_0 t +(1)/( 6) bt ^(3) `

B

` v_0 t +(1)/(3) bt^(3) `

C

` v_0 t +(1)/(3) bt^(2)`

D

` v_0 t+(1)/(2) bt^(2) `

Text Solution

Verified by Experts

The correct Answer is:
A
` a= (dv)/(dt)= bt rArr int _(v_0)^(v) dv =int _0^(t) bt dt rArr v= v_0 +(bt^(2))/( 2) `
` v= (dx)/(dt) =v_0 +(bt^(2))/(2) rArr int _0 ^(x) dx =int _0 ^(t) (v_0 +(bt^(2))/(2)) dt rArr x = v_0t +(bt^(3))/(6) `
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