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

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

1.	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
Answer» Solution :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`