AP Calculus BC 4.2 Motion Rates Overview

Review motion-rate questions by linking position, velocity and acceleration functions to direction and turning behaviour.

Covered syllabus points

CHA-3.B—Calculate rates of change in applied contexts

[Maximum number: 2]

Johanna jogs along a straight path. For $0 \leq t \leq 40$ , Johanna's velocity is given by a differentiable function v. Selected values of v(t), where t is measured in minutes and v(t) is measured in meters per minute, are given in the table above.

Bob is riding his bicycle along the same path. For $0 \leq t \leq 10$ , Bob's velocity is modeled by $B(t)=t^{3}-6 t^{2}+300$ , where t is measured in minutes and B(t) is measured in meters per minute. Find Bob's acceleration at time t=5.

Bob's acceleration is $B^{\prime}(t)=3 t^{2}-12 t$ .

B^{\prime}(5)=3(25)-12(5)=15 \text { meters } / \mathrm{min}^{2}

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Covered syllabus points

4.2 Straight-Line Motion: Connecting Position, Velocity, and Acceleration question 1