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_(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=bt`
`therefore int_(upsilon_(0))^(upsilon)d upsilon=int adt = int_(0)^(1) bt.dt`
`therefore upsilon=upsilon_(0)+(bt^(2))/(2)`
Further integrating we get,
`s=upsilon_(0)t+(bt^(3))/(6)`