Question

A particle starts at the origin and initial verlocity is i - j + 3k. Its acceleration is a(t) = 6t i + 12t^2 j + 6t k. Find its position function.

I need help confirming my answer.

Is the correct way to do this to integrate a(t) to get velocity and then integrate velocity to get position?

Answer 1

yeah. You are also given it's initial velocity

Answer 2

When finding velocity I need to use the initial velocity as the C right?

Answer 3

Yes, the constant of integration after the first integration is your initial velocity

Answer 4

My final answer is

(t^3 + t)i + (t^4 -t)j + (2/3 t^3 + 3t)k + c (c = 0 because we started at the origin)

Answer 5

hang on...i'll check and see what I get

Answer 6

I get
s(t)=(t^3+t)i+(t^4-t)j+(t^3-3t)k

Answer 7

Ah. I see what I did wrong. Thank you for your help! I looked at the wrong numbers for k when I was dong position integral. It works for me now.

Answer 8

cool, no prob