Free response with a graphing calculator (Part A)
BC: Particle moving in the plane
- Unit 9
- 9 points
- About 15 minutes
- BC only
You can use a calculator on this question, just like on exam day.
A multi-part problem, usually set in a real-world context, where you need a graphing calculator for things like definite integrals, derivatives at a point and solving equations. You show your setup, give decimal answers to three places, and explain or justify your conclusions. On the exam: 2 questions in Part A of the free-response section (30 minutes, graphing calculator required). The whole free-response section is 6 questions in 90 minutes and counts for 50% of the score. AB and BC use the same format; on BC, one of these is usually a parametric, polar or vector question.
The question
A particle moves in the xy-plane. Its position at time t, for 0 ≤ t ≤ 4, is (x(t), y(t)), where dx/dt = 3 − t·e^(t/4) and dy/dt = 2 sin(1.5t) + 1. At time t = 0, the particle is at the point (1, −2). (Your calculator should be in radian mode.)
Suggested time: 15 minutes
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Part (a)
2 pointsFind the speed of the particle at time t = 1, and find the acceleration vector of the particle at time t = 1.
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Part (b)
2 pointsFind the time t, for 0 < t < 4, at which the line tangent to the path of the particle is vertical. Justify your answer.
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Part (c)
3 pointsFind the position of the particle at time t = 4.
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Part (d)
2 pointsFind the total distance traveled by the particle over the time interval 0 ≤ t ≤ 4.
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