find the velocity vector?

Question

the particle has the given acceleration, initial velocity and position:
a(t)= 16i+48tj+84t^2k
v(0)=i
r(0)=j-k

A. Find the velocity vector
B. Find the position vector

ok i know that a(t)=v'(t) and v(t)=r'(t)
i thought i could just take the antideriv of a(t) and then v(t) but i didn't get the right answer.

Answer 1

How about this?
integrate a(t) wrt t
v(t) = 16t i + 48t^2/2 j + 84t^3/3 + c
v(0) = i so c = i
v(t)= (16t +1)i + 24t^2 + 28t^3

integrate v(t) wrt t
r(t) = (t + 16t^2/2) i + 24t^3/3 j + 28t^4/4 k + c
r(0) = j - k
r(t) = (t + 8t^2) i + (8t^3 + 1) j + (7t^4 -1) k