Translation between representations (TBR)
Cart pushed by a force that varies with time
- Units 3 and 4
- 12 points
- About 28 minutes
You can use a calculator on this question, just like on exam day.
A multipart problem about one situation shown in several ways. You draw a diagram, derive equations, sketch or draw graphs, and then explain whether your answers agree with each other or use them to predict what happens when the situation changes. On the exam: Question 2 of 4. New for May 2027: the free-response section is 95 minutes, down from 100, for all 4 questions (50% of your score), one of each type in this order. Calculator and equation sheet allowed. The CED suggests 25–30 minutes. This question type started in May 2025, so Physics C: Mechanics free-response questions from 2024 and earlier are built differently.
The question
A cart of mass 2.0 kg is at rest on a horizontal, frictionless track. Starting at t = 0, a horizontal net force acts on the cart, given by , where F is in newtons and t is in seconds, for 0 ≤ t ≤ 4.0 s. After t = 4.0 s the force is zero.
Suggested time: 28 minutes
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Part (a)
2 pointsDescribe the graph of the force on the cart as a function of time from t = 0 to t = 4.0 s. Include the axes, labels with units, the shape, and key values.
Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).
0 / 2,500 characters
Part (b)
2 pointsDerive an expression for the impulse delivered to the cart from t = 0 to time t, for 0 ≤ t ≤ 4.0 s. Then calculate the cart's speed at t = 4.0 s.
Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).
0 / 2,500 characters
Part (c)
3 pointsDerive an expression for the cart's velocity v(t) for 0 ≤ t ≤ 4.0 s. Then describe the graph of v as a function of time from t = 0 to t = 6.0 s, including its shape, its slope at key times, and key values.
Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).
0 / 2,500 characters
Part (d)
1 pointCalculate the work done on the cart by the force from t = 0 to t = 4.0 s.
Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).
0 / 2,500 characters
Part (e)
2 pointsBetween t = 2.0 s and t = 4.0 s the force on the cart is decreasing. Explain how your force graph from part (a) is consistent with your velocity graph from part (c) during this interval.
Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).
0 / 2,500 characters
Part (f)
2 pointsCalculate the average power delivered to the cart by the force from t = 0 to t = 4.0 s, and the instantaneous power delivered at t = 2.0 s.
Type math plainly, like x^2, sqrt(x) or (x+1)/(x−1).
0 / 2,500 characters
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