How do you find total distance traveled using anitdifferentiation? Solution The

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The function s(t) describes the position of a particle moving along a coordinate line, where s is in feet and t is in seconds. s(t) = t^4-4t^2+4 , t >= 0 Displacement from t=0 to t=5 is simply s(5)-s(0) = (5^4 - 4*5^2 + 4) - (0 + 0 + 4) = 625 - 100 = 525 feet ---------------- Art Vandelay is right: s(t) = t^4-4t^2+4 v(t) = s'(t) = 4t^3 - 8t = 0 at t=0 and t=v2 Distance covered from t=0 to t=v2 is |s(v2)-s(0)| Distance covered from t=v2 to t=5 is |s(5)-s(v2)| Total distance covered form t=0 to t=5 is |s(v2)-s(0)| + |s(5)-s(v2)| = |4 - 4×2 + 4 - 4| + |(625 - 100 + 4) - (4 - 4×2 + 4)| = |- 4| + |529 - 0| = 4 + 529 = 533 feet

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