Thread: Vector-valued functions and motion in space

1. Vector-valued functions and motion in space

This is probably a simple question but:

r(t) is the position of a particle in the xy-plane at time t. Find an equation in x and y whose graph is the path of the particle. Then find the particle's velocity and acceleration vectors at the given time t.

$r(t)=(t+1)i+(t^{2}-1)j, t=1$

Ok, I know how to find the velocity and acceleration vectors at the given time, but I'm not sure how to do the part in bold. The answer given in the book is $y=x^{2}-2x$ but I don't understand they arrived at that. Any help would be appreciated. Thanks

2. What they're doing is eliminating the parameter $t$. That is, you have the equations

$x=t+1$

$y=t^{2}-1.$

Eliminate the parameter $t$ to arrive at only one equation. Do you have any ideas on how to proceed?

3. It's from the point that you just posted that I'm not sure what to do. Sorry, I should've been more specific.

Nevermind, I'm an idiot. Just solve the first equation for t and plug into the second equation. Thanks a lot. I guess I should've thought about it a bit more.

4. Try solving the first equation for $t$. What do you suppose you could do with it after you do that?