???Position Vectors-integration??? ?

Question

I have the acceleration vector in terms of t, a(t). I have r(t) at t=0. Can someone explain in detail how to get the velocity and position vectors of this particle in terms of t.

Answer 1

Take the integral of a(t)dt; this will involve a constant of integration and the integral is the velocity v(t).  (It would be nice if you had v(0) to find the constant of integration.)  One more integration will give you r(t), and you can use r(0) to find the new constant of integration.