Скачать или смотреть 2024 AP Calculus AB FRQ #2

A particle moves along the x-axis so that its velocity at time t is greater than/equal to 0 is given by v(t) = ln(t^2 - 4t + 5) - 0.2t.

(a) There is one time, t = tR, in the interval t is between 0 and 2 when the particle is at rest (not moving). Find tR. For t is between 0 and tR, is the particle moving to the right or to the left? Give a reason for your answer.
(b) Find the acceleration of the particle at time t = 1.5. Show the setup for your calculations. Is the speed of the particle increasing or decreasing at time t = 1.5? Explain your reasoning.
(c) The position of the particle at time t is x(t), and its position at time t = 1 is x(1) = −3. Find the position of the particle at time t = 4. Show the setup for your calculations.
(d) Find the total distance traveled by the particle over the interval t is between 1 and 4. Show the setup for your calculations.

Problem A: 00:05
Problem B: 03:41
Problem C: 08:45
Problem D: 11:14