2018年AP微积分AB简答题真题+答案+PDF下载
1. People enter a line for an escalator at a rate modeled by the function r given by
where r(t) is measured in people per second and t is measured in seconds. As people get on the escalator, they exit the line at a constant rate of 0.7 person per second. There are 20 people in line at time t = 0.
(a) How many people enter the line for the escalator during the time interval 0 ≤ t ≤ 300 ?
(b) During the time interval 0 ≤ t ≤ 300, there are always people in line for the escalator. How many people are in line at time t = 300 ?
(c) For t > 300, what is the first time t that there are no people in line for the escalator?
(d) For 0 ≤ t ≤ 300, at what time t is the number of people in line a minimum? To the nearest whole number, find the number of people in line at this time. Justify your answer.
2. A particle moves along the x-axis with velocity given by v(t)=10sin(0.4t2)/t2-t+3 for time 0≤t ≤3.5. The particle is at position x = −5 at time t = 0.
(a) Find the acceleration of the particle at time t = 3.
(b) Find the position of the particle at time t = 3.
(c) Evaluate∫3.50v(t)dt , and evaluate ∫3.50|v(t)|dt. Interpret the meaning of each integral in the context of the problem.
(d) A second particle moves along the x-axis with position given by x2(t) = t2− t for 0≤t≤3.5. At what time t are the two particles moving with the same velocity?
2018年AP微积分AB简答题真题余下省略！
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