2019 AP Calculus AB FRQ #2

The velocity of a particle, P, moving along the x-axis is given by the differentiable function P(v), where P(v((t)) is measured in meters per hour and t is measured in hours. Selected values of P(v((t) are shown in the table above. Particle P is at the origin at time t = 0.
(a) Justify why there must be at least one time t, for 0.3 to 2.8, at which P(v((t)), the acceleration of particle P, equals 0 meters per hour per hour.
(b) Use a trapezoidal sum with the three subintervals [0, 0.3], [0.3, 1.7], and [1.7, 2.8] to approximate the value of ∫ P(v(t)) dt from 0 to 2.8.
(c) A second particle, Q, also moves along the x-axis so that its velocity for 0 to 4 is given by Q(v(t)) = 45 * cos(0.063 * t^2) meters per hour. Find the time interval during which the velocity of particle Q is at least 60 meters per hour. Find the distance traveled by particle Q during the interval when the velocity of particle Q is at least 60 meters per hour.
(d) At time t = 0, particle Q is at position x = −90. Using the result from part (b) and the function vQ from part (c), approximate the distance between particles P and Q at time t = 2.8.
Timestamps
Intro: 00:00
Part a: 00:23
Part b: 02:39
Part c: 07:37
Part d: 11:50