2023 AP Calculus AB FRQ #2

Stephen swims back and forth along a straight path in a 50-meter-long pool for 90 seconds. Stephen’s velocity is modeled by v(t) = 2.38e^(-0.02*t) * sin(pi/56 * t), where t is measured in seconds and v(t) is measured in meters per second.
(a) Find all times t in the interval t is between 0 and 90 at which Stephen changes direction. Give a reason for your answer.
(b) Find Stephen’s acceleration at time t = 60 seconds. Show the setup for your calculations, and indicate units of measure. Is Stephen speeding up or slowing down at time t = 60 seconds? Give a reason for your answer.
(c) Find the distance between Stephen’s position at time t = 20 seconds and his position at time t = 80 seconds. Show the setup for your calculations.
(d) Find the total distance Stephen swims over the time interval t is between 0 and 90 seconds. Show the setup for your calculations
Intro: 00:00
Problem a: 00:19
Problem b: 02:16
Problem c: 06:14
Problem d: 12:41