A particle moves along a straight track so that its velocity
MATHEMATICS · Multi-part · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation
Problem
A particle moves along a straight track so that its velocity, in meters per second, is given for 0≤t≤4 seconds by v(t)=3t2−12t+9. The position at t=0 is x=0.
(1) Part 1: Calculate the particle’s acceleration a(t) for 0≤t≤4 and state its units.
(2) Part 2: Determine the time intervals on which the particle is speeding up and the intervals on which it is slowing down. Clearly explain your reasoning.
(3) Part 3: Evaluate the acceleration at t=1 and t=3. Interpret each value in the context of the motion.