Acceleration of a particle at any time t is `(2thati+3t^(2)hatj)m//s^(2)`. If initially particle is at rest, find the velocity of the particle at time `t=2s`

Explanation

Here acceleration is a function of time,
i.e, acceleration is not constant . So , we can not apply `vecv=vecu+vecat`
We will have to go for integration for dinding velocity at any time t . This `dvecv=vecadt`or
`int_(0)^(vecv)dvecv=int_(0)^(2)vecadt"or" vecv=int_(0)^(2)(2thati+3t^(2)hatj)dt=[t^(2)hati+t^(3)hatj]_(0)^(2)=(4hati+8hatj)m//s`
Therefore , velocity of particle at time `=2s is (4hati+8hatj)m//s`