Acceleration of a particle at any time t is `veca=(2thatj+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 cannot apply `vecv=vecu+vecat`
We will have to go for integration for finding velocity at time t.Thus
`dvecv=veca dt` or `underset(0)overset(v)int d vecv=underset(0)overset(2)int veca dt` (or)`vecv=underset(0)overset(2)int (2thati+3t^(2)hatj)` dt `=[t^(2)hati+t^(3)]_(0)^(2)=(4hati+8hatj)m//s`
Therefore,velocity of particle at time t=2 s is =`(4hati+8hatj)m//s`