A capsule is approaching a space station. Starting at time t0 = 3 s it has initial position r0 = 4 m i 7 m j 2 m k and velocity v0 = 4 m s i. It then starts a burn which gives it acceleration a = 2 m s3t k. (a) Find its position vector r(t) as a function of time for all times t after t0.

(b) What if the acceleration was a = 2 m s3t k?