# Homework Help: Quick Solve - Literally Stuck at the Last Step

1. Apr 11, 2010

### IntegrateMe

The position of a particle moving in the xy-plane is given by the parametric equations x = t3 - 3t2 and y = 2t3 - 3t2 - 12t. For what values of t is the particle at rest?

So we're trying to find when the slope (dy/dx) is equal to 0.

dy = 6t2 - 6t - 12
dx = 3t2 - 3t

dy/dx = (6t2 - 6t - 12) / (3t2 - 3t)
dy/dx = [6(t2 - t - 2)] / [3t(t - 2)]
dy/dx = [2(t + 1)(t - 2)] / [t(t -2)]
dy/dx = 0 @ t = -1 or 2

So, i would assume the answer is "-1 or 2" but the answer is really just "2 only". Can anyone explain this to me?

2. Apr 11, 2010

### Gregg

Assuming t is the time, if you find multiple values in the result you will discard the ones that are not useful, like the idea of something taking a negative amount of time.

3. Apr 11, 2010

### IntegrateMe

Wow, that was simple. I'm sorry but i should've seen how obvious that was. Thanks a bunch!
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