Finding the Position of a Spaceship with Given Acceleration and Velocity Vectors

[Timebomb3750]

Finding a position vector...

Homework Statement

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

Homework Equations

uhhh...

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?

 

[M Quack]

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

 

[Timebomb3750]

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. :)