The total distance traveled by an object moving at velocity (t) from the time t a

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The total distance traveled by an object moving at velocity υ(t) from the time t " a to the time t = b is

 x(b) lv(t)l dt + x(a) a ||


The absolute value |υ(t)| is used to account for the possibility that υ(t) might be negative. Suppose an object starts at time t = 0 and moves with a velocity of υ(t) = cos(πt) m. Find the object’s location at t = 1 s if x(0) = 2 m.

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