A point moves along the x-axis, and its position, x, at time t seconds is given by p(t) = t^3 – 6t^2 + 5. Find the total distance the point travels from t = – 1 to t = 6.
To put it in a single statement, what you are looking for is:Originally Posted by bobby77
In other words, we need to find out if and where the object turns around.
The velocity has zeros at t = 0 s and t= 4 s. Since v(t) is positive at t = -1, the object starts moving from position -2 and moves in the +x direction to t = 0 s at position 5 (7 units total distance) and turns around. It goes in the -x direction to t = 4 s at position -27 (34 units total distance) and turns around. It goes in the +x direction to t = 6 s at position 5 (66 units total distance.) So the object moves a total of 66 units.
What? Did you trademark it when I wasn't looking?
To all who post here: I learned the previous integral form from ThePerfectHacker!
(I promise I'll pay you a tithe from any moneys I get from answering bobby77's question. Would you prefer cash or credit? )