# Interval when moving to right and left?

• Oct 17th 2011, 01:17 PM
kmjt
Interval when moving to right and left?
Determine the time interval on which the point is moving to the right and to the left.

Point P is moving along the x axis so that its position x at time t is given by x=3t^3-4t+1

So I determined the velocity and accleration equations:

v(t) = 3t^2-4
a(t) = 6t

But I have no clue how to determine what time intervals which the point is moving to the right or to the left?
• Oct 17th 2011, 01:25 PM
emakarov
Re: Interval when moving to right and left?
If x(t) = 3t^3 - 4t + 1, then v(t) = 9t^2 - 4.

The points is moving right when v(t) > 0 and left when v(t) < 0.
• Oct 18th 2011, 01:00 AM
kmjt
Re: Interval when moving to right and left?
Oops the first function before velocity was actually supposed to be x = t^3 -4t +1

But how would I determine when v(t) > 0 and when v(t) < 0?
• Oct 18th 2011, 01:04 AM
emakarov
Re: Interval when moving to right and left?
Quote:

Originally Posted by kmjt
But how would I determine when v(t) > 0 and when v(t) < 0?

Here is a tutorial on solving quadratic inequalities.