1. ## Motion Problem

Starting at $t = 0$ a particle moves along the $x$ axis so that it's position at time $t$ is given by $x(t) = t^{4} - 5t^{2} + 2t$. For what values of $t$ does that particle take while moving to the left?

Answer: $0.203 < t < 1.470$

Any starting hints on how this came to be? Note: This is the complete problem given.

Perhaps the answer is to simply graph the function Then you can see what values the function takes as it goes left from $0$.

But the problem is that a graph goes on forever to the left. So how can there be a left interval?

But perhaps this is some kind of flipped graph, where time is on the $y$ axis rather than the $x$ one. Yeah, I think that's the problem.

2. ## Re: Motion Problem

hey Jason76.

Hint: Do you know how to use calculus to find the minimum and maximum of a function in a given region?

3. ## Re: Motion Problem

If the particle is moving to the left that means its velocity is negative. The function you were given is the position of the particle; hence the derivative of the function with respect to time gives its velocity. So take the derivative, plot that and and see where it is negative. The derivative will be a cubic function, which you should know takes a general shape of a "sideways S." It appears from the answer that t is limited to positive values only.