1. ## Integral/Displacement Problem

A particle moves in a straight line with velocity ft/s. Find the total displacement and total distance traveled over the time interval .
I solved the displacement however I'm not sure how to find the total distance traveled. Thanks to anyone who can help!

2. The distance is the integral of the speed or |v(t)|

1/t^2 -1/25 which is >0 for 3 < t < 5 and <0 5 < t < 6

you have integral(1/t^2 -1/25) 3 < t < 5 and
integral(1/25 -1/t^2) 5 < t < 6

3. Dear Casas4,

Since the velocity time graph is negative in the interval, (5,6] and positive in the interval, [3,5)

Total distance traveled = $\left|\int_{3}^{5}{(t^{-2}-\frac{1}{25})}\right|+\left|\int_{5}^{6}{(t^{-2}-\frac{1}{25})}\right|$

Hope this helps.