The acceleration of a particle increasing linearly with timer is be. The particle starts from the origin with an initial velocity, The distance travelled by the particle in time will be

Options

A. `v_(0)t+(1)/(6)bt^(3)`
B. `v_(0)t+(1)/(3)bt^(2)`
C. `v_(0)t+(1)/(3)bt^(3)`
D. `v_(0)t+(1)/(2)bt^(2)`

Answer

a

Explanation

Here acceleration a=bt
`(dv)/(dt)=bt` or dv=bt dt
`int_(v_0)^(v) dv=int_(0)^(t) bt dt` or `v-v_0=(bt^(2))/(2)`
`v=v_(0)+(bt^2)/(2)`
`dx=v_0 dt(bt^2)/(2)dt`
`x=v_0 t+(1)/(2)(bt^3)/(3)=v_0t(bt^3)/(6)`