Grade 10 Physical Sciences · Mechanics

Calculate from a motion graph

Work out values from a motion graph, for example velocity from the gradient of a position-time graph or displacement from the area under a velocity-time graph.

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Exam Velocity Time Graph Grade 10Kevinmathscience

GCSE Physics - Velocity-Time Graphs - How to Find Acceleration & Distance Travelled (2027/28 exams)Cognito

Graphs of Motion Velocity vs Time Graph past paper questionMiss Martins Maths and Science

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Question 4.3 · November 2022 · Paper 1 · Provincial · 4 marks

Study the velocity versus time graph below for the motion of a car travelling east. Diagram for this question

4.3 Calculate the acceleration of the car between D and E.(4)

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More past paper questions: calculate from a motion graph

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3. Question 5.1.3 · November 2023 · Paper 1 · Provincial · 4 marks
5.1 The velocity versus time graph below illustrates the motion of an object that is initially travelling east. At $t = 0$ s, the position of the object is zero.

Answer the questions that follow.
5.1.3 Calculate the acceleration of the object for interval B – D.(4)
Show the memo (4 ticks)Memo
1. ✓
  Gradient formula $a = \frac{y _{2} - y _{1}}{x _{2} - x _{1}}$
  1 mark · Calculate from a motion graph
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  Substitution $a = \frac{- 10 - 10}{7 - 3}$
  1 mark · Calculate from a motion graph
3. ✓
  Magnitude with unit $a = - 5$ m·s $^{- 2}$
  $a = 5$ m·s $^{- 2}$
  1 mark · Calculate from a motion graph
4. ✓
  Direction $a = 5$ m·s $^{- 2}$ west
  1 mark · Calculate from a motion graph
4. Question WE4 · Siyavula Grade 10 Physical Sciences, 21.6 Description of motion, Worked example 4 · 6 marks
WE4 The velocity vs. time graph of a truck is plotted below. Calculate the distance and displacement of the truck after $15$ seconds.(6)
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1. ✓
  Area 0 to 5 s $Area_{△} = \frac{1}{2} b \times h = \frac{1}{2} \times 5 s \times 4$ m·s $^{- 1}$ $= 10$ m
  1 mark · Calculate from a motion graph
2. ✓
  Area 5 to 12 s $Area_{□} = l \times b = 7 s \times 4$ m·s $^{- 1}$ $= 28$ m
  1 mark · Calculate from a motion graph
3. ✓
  Area 12 to 14 s $Area_{△} = \frac{1}{2} \times 2 s \times 4$ m·s $^{- 1}$ $= 4$ m
  1 mark · Calculate from a motion graph
4. ✓
  Area 14 to 15 s $Area_{△} = \frac{1}{2} \times 1 s \times 2$ m·s $^{- 1}$ $= 1$ m (below the time axis)
  1 mark · Calculate from a motion graph
5. ✓
  Distance $D = 10 + 28 + 4 + 1 = 43$ m
  1 mark · Calculate from a motion graph
6. ✓
  Displacement $Δ x = 10 + 28 + 4 - 1 = 41$ m in the positive direction
  1 mark · Calculate from a motion graph
5. Question a · Siyavula Grade 10 Physical Sciences, 21.6 Description of motion, Worked example 5 · 2 marks
The position vs. time graph below describes the motion of an athlete.
a What is the velocity of the athlete during the first $4$ seconds?(2)
Show the memo (2 ticks)Memo
1. ✓
  Gradient $v = \frac{Δ x}{Δ t} = \frac{4 m - 0 m}{4 s - 0 s}$
  1 mark · Calculate from a motion graph
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  Answer $v = 1$ m·s $^{- 1}$
  1 mark · Calculate from a motion graph
6. Question WE6 · Siyavula Grade 10 Physical Sciences, 21.6 Description of motion, Worked example 6 · 4 marks
WE6 The acceleration vs. time graph for a car starting from rest, is given below. Calculate the velocity of the car and hence draw the velocity vs. time graph.(4)
Show the memo (4 ticks)Memo
1. ✓
  Change in velocity 0 to 2 s $Δ v = Area = l \times b = 2 s \times 2$ m·s $^{- 2}$ $= 4$ m·s $^{- 1}$
  1 mark · Calculate from a motion graph
2. ✓
  Change in velocity 2 to 4 s $Δ v = 2 s \times 0$ m·s $^{- 2}$ $= 0$ m·s $^{- 1}$ , so the velocity stays constant at $4$ m·s $^{- 1}$ .
  1 mark · Calculate from a motion graph
3. ✓
  Change in velocity 4 to 6 s $Δ v = 2 s \times (- 2$ m·s $^{- 2}$ $) = - 4$ m·s $^{- 1}$ , so the velocity decreases from $4$ m·s $^{- 1}$ to $0$ m·s $^{- 1}$ at $t = 6$ s.
  1 mark · Calculate from a motion graph
4. ✓
  Velocity vs. time graphStraight line from $0$ to $4$ m·s $^{- 1}$ between $0$ and $2$ s; horizontal at $4$ m·s $^{- 1}$ from $2$ s to $4$ s; straight line down to $0$ m·s $^{- 1}$ at $6$ s.
  1 mark · Sketch motion graphs

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