MATHEMATICS · Multi-part · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation
Problem
The position, x (in m), of an object that moves along a straight line is changing with time, t (in s), as x=16−12t+2t2.
(1) Make a plot of velocity vs. time from t=0 to t=6s
(2) Make a plot of acceleration vs. time from t=0 to t=6s
(3) When is the velocity zero and what then is the position of the object?
(4) What is the average velocity between t=−1 to t=3.
(5) At what time the object reverses its direction.
(6) What is the average speed between t=0 to t=6.