Asked by Audrey
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.
Answers
Answered by
Steve
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
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
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