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

Acceleration of a particle at any time t is veca=(2thati+3t^(2)hatj)m/

1.	Acceleration of a particle at any time t is veca=(2thati+3t^(2)hatj)m//s^(2).If initially particle is at rest, find the velocity of the particle at time t=2s
Answer» Solution :Here acceleration is a function of time , i.e., acceleration is not constant . So , we cannot APPLY `vecv=vecu+vecat` We will have to ho for integration for finding velocity at time t. thus `dvecv=vecadt "or" int_(0)^(v) d vecv=int_(0)^(2)veca dt "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 `t=2 s is =(4hati+8hatj)m//s`