help with finding r(t) from r''(t)

[Guest]

Hi
Here is the problem:

These are all vectors by the way:

Find r(t) if r''(t) = (t, t^2, cos(2t))

r'(o) = (1, 0, 1) and r(0) = (0, 1, 0)

I have this so far:

1st = r'(t) = (t^2/2, t^3/3, sin(2t)/2) which equals:
2nd = r'(t) = (1 + t^2/2)i + (t^3/3)j + (1 + sin(2t)/2)k

My question is this:
Do I get the integral of the 2nd equation or the 1st to find r(t)?

Thanks for your help
Take care,
Beckie

 

[stapel]

Have you taken the constants of integration into account, solving for their values by using the given specific points? For instance, for r'(t), shouldn't you have:

. . . . .r'(t) = [(1/2)t² + C, (1/3)t³ + D, -(1/2)sin(2t) + E]

. . . . .r'(0) = [0 + C, 0 + D, 0 + E] = [1, 0, 1]

...and then solve for C, D, and E...?

Eliz.