Motion in the xy-plane

**aeubz** · September 13th 2008, 05:29 PM

I need help with this problem.. it asks me for the accleration and velocity and i already know to find those i need to take the first and second derivatives. but the part i don't get is "Find an equation in x and y whose graph is the path of the particle."

r(t) = (t+1)i + ((t^2)-1)j

**topsquark** · September 13th 2008, 05:39 PM

Originally Posted by aeubz

I need help with this problem.. it asks me for the accleration and velocity and i already know to find those i need to take the first and second derivatives. but the part i don't get is "Find an equation in x and y whose graph is the path of the particle."

r(t) = (t+1)i + ((t^2)-1)j

The x component of r(t) would be x(t), so $x(t) = t + 1$ . Similarly $y(t) = t^2 - 1$ . This is a parametric set of equations describing the curve. Do you know how to eliminate the parameter?

-Dan

**Soroban** · September 13th 2008, 05:43 PM

Hello, aeubz!

Find an equation in $x$ and $y$ whose graph is the path of the particle:
. . . $r(t) \;= \;(t+1)i + (t^2-1)j$

We have parametric equations: . $\begin{Bmatrix}x &=& t + 1 & {\color{blue}[1]}\\ y &=& t^2-1 & {\color{blue}[2]} \end{Bmatrix}$
Eliminate the parameter.

Solve [1] for $t\!:\;\;t \:=\:x-1$

Substitute into [2]: . $y \:=\<img src=$ x-1)^2 + 1" alt="y \:=\

x-1)^2 + 1" />

Therefore: . $y \;=\;x^2 - 2x + 2$

**aeubz** · September 13th 2008, 06:03 PM

thanks! you mean y = x^2 - 2x , but thank you for the help!

**topsquark** · September 13th 2008, 07:29 PM

Originally Posted by aeubz

thanks! you mean y = x^2 - 2x , but thank you for the help!

No he didn't.
$(x - 1)^2 + 1 = (x^2 - 2x + 1) + 1 = x^2 - 2x + 2$

-Dan

Thread: Motion in the xy-plane

LinkBack

Thread Tools

Display

Motion in the xy-plane

Similar Math Help Forum Discussions

Motion in the xy-plane -- ahhhh

Numerical Problem for motion along a plane (HELP)

Numerical Problem for motion along a plane (HELP) -2-

Plane motion w/ parametric equations

Smooth Pulleys and motion on an inclined plane

Search Tags