Motion Analysis Example

AP Calculus · Axiom Academy

Example Motion Analysis Example Analyzing particle motion using position, velocity, and acceleration v(t) = s'(t) = 6t^2 - 18t + 12 = 6(t-1)(t-2) Particle is at rest when v(t) = 0 : at t = 1 and t = 2 . v(t) > 0 on : moving right. v(t) < 0 on (1,2) : moving left. At t = 0.5 : v > 0 , a = -12 At t = 1.5 : v At t = 3 : v > 0 , a > 0 → speeding up. s(0) = 0 , s(1) = 5 , s(2) = 4 , s(3) = 9 . Total distance from t=0 to t=3 : |5-0| + |4-5| + |9-4| = 5 + 1 + 5 = 11 . What is the total distance traveled from t=0 to t=3 ? You've worked through the full solution. Review each step to solidify your understanding.

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