2025 AP Calc AB Free Response Question #5

This FRQ from the 2025 AP Calculus AB set presents us with a position function for particle H and a velocity function for particle J. In part a, we take a derivative to determine the velocity of particle H at time 2. In part b, we use a sign chart for velocity to determine intervals where the particles are moving in opposite directions. In part c, we use both velocity and acceleration to determine whether particle J has its speed increasing or decreasing at a certain time. In part d, we use an initial position and compute a definite integral using a u-substitution to determine the position of particle J at time 2.