Free response with a graphing calculator (Part A)
Particle motion with a calculator
- Units 4, 5 and 8
- 9 points
- About 15 minutes
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 along the x-axis. Its velocity at time t, for 0 ≤ t ≤ 6, is given by v(t) = 2 sin(e^(t/4)) + 1. At time t = 0, the particle is at position x = 3. (Your calculator should be in radian mode.)
Suggested time: 15 minutes
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Part (a)
2 pointsFind the acceleration of the particle at time t = 5.5. Is the speed of the particle increasing or decreasing at time t = 5.5? Give a reason for your answer.
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Part (b)
2 pointsFind the total distance traveled by the particle over the time interval 0 ≤ t ≤ 6.
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Part (c)
2 pointsFind the position of the particle at time t = 6.
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Part (d)
3 pointsFind the greatest position of the particle, that is, the largest value of x(t), for 0 ≤ t ≤ 6. Justify your answer.
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