# Homework Help: Finding a position vector

1. Feb 25, 2012

### Timebomb3750

Finding a position vector....

1. The problem statement, all variables and given/known data
A spaceship is traveling with acceleration a(t)=<e^(t) , t , sin2t>. At t=0, the spaceship was a origin r(0)=<0,0,0> and had an initial velocity of v(0)=<1,0,0> Find the position of the ship at t=pi

2. Relevant equations

uhhh...

3. The attempt at a solution

I figured I'd work backwards with the acceleration vector given to find the velocity and position vectors, then put the t=pi into the position vector I find.

So, v(t)=<e^(t) , (1/2)t^(2) , -(1/2)cos(2t)>
Then r(t)=<e^(t), (1/6)t^(3) , -(1/4)sin(2t)>

But this doesn't seem right to me because when I put in the given t=0 into my v(t), I get <1,0,-(1/2)> not the <1,0,0> like the problem says. I'm approaching this problem wrong, aren't I?

2. Feb 25, 2012

### M Quack

Re: Finding a position vector....

No, you are doing fairly well. What would happen if you added a constant to the velocity?

3. Feb 25, 2012

### Timebomb3750

Re: Finding a position vector....

Okay, I have it figured out.

v(t)=<e^(t) , (1/2)t^2 , (-1/2)cos(2t)+(1/2)> So that V(0)=<1,0,0>

Then, I find r(t) which is equal to <e^(t)-1 , (1/6)t^3 , (-1/4)sin(2t)+(1/2)t> So that r(0)=<0,0,0>

Then I plug in pi into my r(t) which comes out to be r(pi)=<e^(pi)-1 , (1/6)pi^3 , (pi/2)> Please tell me this is right. :)