Question

A particle moves according to the equation of motion s(t)=t^2-2t+3 where s(t) is measured in feet and t is measured in seconds. Find the total distance traveled in the 3 seconds.

Answer 1

If you just integrate the velocity, you wind up with the final displacement, not the distance traveled. So, to avoid subtracting backward motion, use the absolute value of the velocity:

v(t) = 2t-2
distance = ∫[0,3] |2t-2| dt

http://www.wolframalpha.com/input/?i=%E2%88%AB%5B0,3%5D+%7C2t-2%7C+dt