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

Options

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) `

Answer

A

Explanation

` 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) `