Question

A particle moves along the x-axis so that at any time t its position is given by x(t)=(t^2-1)^2. For what values of t is the particle moving left?

Answer 1

help please!!

Answer 2

Let time t be the independent variable. Then you can graph the function x(t) on an x-y plane. Assuming positive is right and negative is left, then you are looking at how the position is changing. If the function is increasing, then its position is increasing so it's going to the right. Opposite is true so decreasing -> left. This will be easy to see on the graph - just look at when it's pointing down. Or, you can do some fancy derivative stuff and see when the rate of change is positive or negative, but that's beyond me.

http://www.wolframalpha.com/input/?i=x%28t%29%3D%28t%5E2-1%29%5E2

Answer 3

Thank You!!!!