Please help - Vectors (Mathematics)?

Question

Practice exam question. A particle traces out a curve in 3 dimensions. Its position is specified at time t (sec) by its position vector r = 4ti + 2t^2 + k. Distances are in metres from the origin. Find its velocity and acceleration, as vector functions of time.

Answer 1

I think you mean

r = 4ti + 2t^2j + k

v = dr/dt = 4i + 4tj

and acc = dv/dt = 4j

  

Answer 2

r = 4ti + 2t^2j + k.

v = dr/dt = 4i + 4tj + 0k

a = dv/dt = 0i + 4j + 0k