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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
Velocity–time graph for a cart on a straight horizontal track01234567−4−3−2−101234time (s)velocity (m/s)
Fig. 8.1The cart's velocity–time graph. The time axis is drawn horizontally through velocity zero and is marked in seconds from 1 to 7; the vertical velocity axis is marked in metres per second from −4 to +4. The plotted line runs horizontally at +3.0 m/s from t = 0 to t = 2.0 s, then falls as a single straight sloping segment, passing through zero, to −3.0 m/s at t = 5.0 s, and then runs horizontally at −3.0 m/s until t = 7.0 s.
free response12 marks

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.

  1. (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
  2. (b)

    Determine Determine the time at which the cart is farthest from its starting point, and determine that distance.

    3 marks
  3. (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
  4. (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
Ready to self-mark?Reveal the detailed answer guide
Answer overviewKey answer: 1 point: a = 0 on 0 ≤ t < 2.0 s and on 5.0 s < t ≤ 7.0 s 1 point: a constant and negative between 2.0 s and 5.0 s 1 point: value stated as −2.0 m/s², from (−3.0 − 3.0)/(5.0 − 2.0)
01

(a)

3 marks

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.

How to approach it

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

    1 point: a = 0 on 0 ≤ t < 2.0 s and on 5.0 s < t ≤ 7.0 s

  2. 2

    1 point: a constant and negative between 2.0 s and 5.0 s

  3. 3

    1 point: value stated as −2.0 m/s², from (−3.0 − 3.0)/(5.0 − 2.0)

02

(b)

3 marks

Determine Determine the time at which the cart is farthest from its starting point, and determine that distance.

How to approach it

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

    1 point: the cart is farthest away when the velocity changes sign, at t = 3.5 s

  2. 2

    1 point: area under the graph from 0 to 3.5 s = (3.0)(2.0) + ½(1.5)(3.0)

  3. 3

    1 point: distance = 6.0 + 2.25 = 8.25 m

03

(c)

3 marks

Sketch Sketch a graph of the cart's position as a function of time over the same interval, taking the starting position as zero.

How to approach it

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

    1 point: straight line of positive constant slope from the origin to (2.0 s, 6.0 m)

  2. 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. 3

    1 point: straight line of constant negative slope after t = 5.0 s

04

(d)

3 marks

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.

How to approach it

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

    1 point: moves in the positive direction at constant speed for the first 2.0 s

  2. 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. 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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