AP · AP 1 · free response
AP Physics 1: Algebra-Based · Question 8
AP Physics 1: Algebra-Based · Original GioPhysics question with a detailed, mark-by-mark answer guide.
- Demand
- demanding
- Marks
- 12
- Topics
- 1
- Answer
- Complete
A cart moves along a straight horizontal track. Its velocity as a function of time is described as follows: from t = 0 to t = 2.0 s the velocity is constant at +3.0 m/s; from t = 2.0 s to t = 5.0 s the velocity decreases uniformly from +3.0 m/s to −3.0 m/s; from t = 5.0 s to t = 7.0 s the velocity is constant at −3.0 m/s.
- (a)
Sketch Sketch a graph of the cart's acceleration as a function of time from t = 0 to t = 7.0 s. Label the value of the acceleration on each interval.
3 marks - (b)
Determine Determine the time at which the cart is farthest from its starting point, and determine that distance.
3 marks - (c)
Sketch Sketch a graph of the cart's position as a function of time over the same interval, taking the starting position as zero.
3 marks - (d)
Describe Describe the motion of the cart in words, making clear the difference between the interval in which it is slowing down and the interval in which it is speeding up.
3 marks
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(a)
Sketch Sketch a graph of the cart's acceleration as a function of time from t = 0 to t = 7.0 s. Label the value of the acceleration on each interval.
List the given quantities with units, identify the required quantity, write the governing relationship before substituting, and keep extra digits until the final line so rounding does not distort the result.
- 1
1 point: a = 0 on 0 ≤ t < 2.0 s and on 5.0 s < t ≤ 7.0 s
- 2
1 point: a constant and negative between 2.0 s and 5.0 s
- 3
1 point: value stated as −2.0 m/s², from (−3.0 − 3.0)/(5.0 − 2.0)
(b)
Determine Determine the time at which the cart is farthest from its starting point, and determine that distance.
List the given quantities with units, identify the required quantity, write the governing relationship before substituting, and keep extra digits until the final line so rounding does not distort the result.
- 1
1 point: the cart is farthest away when the velocity changes sign, at t = 3.5 s
- 2
1 point: area under the graph from 0 to 3.5 s = (3.0)(2.0) + ½(1.5)(3.0)
- 3
1 point: distance = 6.0 + 2.25 = 8.25 m
(c)
Sketch Sketch a graph of the cart's position as a function of time over the same interval, taking the starting position as zero.
List the given quantities with units, identify the required quantity, write the governing relationship before substituting, and keep extra digits until the final line so rounding does not distort the result.
- 1
1 point: straight line of positive constant slope from the origin to (2.0 s, 6.0 m)
- 2
1 point: curve that flattens to a maximum at t = 3.5 s and then falls, with curvature downward throughout 2.0–5.0 s
- 3
1 point: straight line of constant negative slope after t = 5.0 s
(d)
Describe Describe the motion of the cart in words, making clear the difference between the interval in which it is slowing down and the interval in which it is speeding up.
Answer the command word directly and use precise physical vocabulary. Include only the distinct features or facts that earn marks, without burying them in unrelated background information.
- 1
1 point: moves in the positive direction at constant speed for the first 2.0 s
- 2
1 point: from 2.0 s to 3.5 s it still moves in the positive direction but slows, because velocity and acceleration have opposite signs
- 3
1 point: from 3.5 s onward it moves in the negative direction and speeds up until 5.0 s, because velocity and acceleration now have the same sign, then travels at constant speed
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