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

Options

A. `v_0t+1/6bt^3`
B. `v_0t+1/3bt^3`
C. `v_0t+1/3bt^2`
D. `v_0t+1/2bt^2`

Answer

A

Explanation

`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`