Acceleration of a particle at any time t is a¯=2ti^+3t2j^m/s2 . If initially particle is at rest find the velocity of the particle at time t=2 sec

Here acceleration is a function of time. We will have to go for integration for finding velocity at time ‘t’ . Thusdv¯=a¯dt⇒∫0v dv=∫02 adt⇒v¯=∫02 2ti^+3t2j^dt=2t22i^+3t33j^02=t2i^+t3j^02=(4i^+8j^)m/s