OpenRevise GCSE

Viewing as

Student Teacher

Teaching this? The teacher view adds 2 files, the mark schemes and the model answers.

Physics · Forces

Distance–time graphs

Draw and interpret distance–time graphs and use gradients to find speed (and tangents for accelerating objects at Higher tier).

  • 6 key terms
  • All boards
Download the full pack · 3 files

Warm-up

Answer each one, then check.

  1. 1

    What is the gradient of a graph?

    Show answerHide answer

    Change in y divided by change in x

  2. 2

    What does a horizontal line on a distance-time graph mean?

    Show answerHide answer

    The object is stationary

  3. 3

    What is speed?

    Show answerHide answer

    Distance divided by time

  4. 4

    What is acceleration?

    Show answerHide answer

    Rate of change of velocity

  5. 5

    What does a steeper line mean?

    Show answerHide answer

    A faster speed

Learning Objectives

  1. 1Draw distance–time graphs from measurements.
  2. 2Interpret lines and slopes of distance–time graphs.
  3. 3Calculate speed from the gradient of a distance–time graph.
  4. 4Find the speed of an accelerating object at an instant using a tangent (Higher tier).

DISTANCE–TIME GRAPHS

The gradient of a distance–time graph is the speed of the object.

A straight line means constant speed, a horizontal line means stationary, and a curve means the speed is changing.

What the Graph Shows

Learn these.

  • Straight line sloping up

    Meaning: Constant speed

  • Horizontal line

    Meaning: Stationary

  • Steeper line

    Meaning: Higher speed

  • Curve getting steeper

    Meaning: Accelerating

  • Curve getting shallower

    Meaning: Decelerating

Speed from a Gradient

An object travels 40 m in the first 20 s. Calculate its speed from the graph.

Show the solutionHide the solution
  1. 1 Gradient \(\dfrac{\text{change in distance}}{\text{change in time}}\)
  2. 2 Substitute \(\dfrac{40}{20}\)
  3. 3 Answer \(2.0\) m/s

Answer2.0 m/s

Describing a Journey

Describe the motion shown from 20 s to 40 s where the line is horizontal.

Show the solutionHide the solution
  1. 1 Distance Does not change
  2. 2 Speed Zero

AnswerThe object is stationary.

Tangent (Higher)

The distance is given by s = 0.5t² (in metres, t in seconds). Find the speed at t = 6 s using a tangent.

Show the solutionHide the solution
  1. 1 Draw a tangent Touching the curve at t = 6 s
  2. 2 Gradient of the tangent \(\dfrac{\Delta s}{\Delta t}\) from two points on the tangent: about \(6\) m/s
  3. 3 Check The speed is t = 6 m/s from s = 0.5t²

AnswerAbout 6 m/s.

Drawing Graphs

Good practice.

  • Axes

    Time on the x-axis, distance on the y-axis, with units.

  • Points

    Plot from a table, then join with a ruler (or a smooth curve if the speed changes).

  • Gradient

    Use a large triangle for accuracy.

  • Units

    m/s if distance in m and time in s.

Story Graph

A cyclist travels 100 m in 20 s, stops for 20 s and then travels 60 m in 20 s. Sketch the graph and calculate the speed in each part.

1. Plot the three sections.

2. Gradient for each.

A good answer shows: Part 1: 5.0 m/s. Part 2: 0 m/s. Part 3: 3.0 m/s.

Can I...?

  1. 1Draw a distance–time graph.
  2. 2Say what a horizontal line means.
  3. 3Calculate speed from a gradient.
  4. 4Compare speeds from slopes.
  5. 5Describe a journey.
  6. 6Describe a curve.
  7. 7Draw a tangent.
  8. 8Use units.

Summary & Exam Focus

  • Gradient = speed.
  • Horizontal line = stationary.
  • Steeper = faster.
  • Higher: tangent to a curve gives instantaneous speed.

Exam focus

The graph shows 100 m in 20 s. Calculate the speed in the first 20 s. (2 marks) (2 marks)

Gradient = distance ÷ time.

Key terms

The vocabulary this lesson expects you to use. Each one is linked from the first place it appears above.

Distance–time graph
A graph of distance against time.
Gradient
How steep a line is.
Stationary
Not moving.
Tangent
A straight line that touches a curve at one point.
Constant speed
The same speed all the time.
Accelerating
Speeding up.

Practice questions

Have a go at each one before you open its answer.

  1. Question 1 Use the graph 4 marks

    The graph shows the distance travelled by a cyclist. (a) Calculate the speed in the first 20 s. (b) Describe the motion between 20 s and 40 s. (c) Calculate the speed between 40 s and 60 s.

    A distance-time graph with a section of constant speed, a stationary section and another section of constant speed.
    Show answerHide answer

    Model answer

    (a) 100 ÷ 20 = 5.0 m/s. (b) Stationary. (c) 60 ÷ 20 = 3.0 m/s.

    Mark scheme

    • 5.0 m/s — 1 mark
    • Stationary — 1 mark
    • Correct distance and time — 1 mark
    • 3.0 m/s — 1 mark
  2. Question 2 State 2 marks

    Describe what the gradient of a distance–time graph represents and what a horizontal line shows.

    Show answerHide answer

    Model answer

    The gradient is the speed. A horizontal line shows the object is stationary.

    Mark scheme

    • Gradient is speed — 1 mark
    • Horizontal line: stationary — 1 mark
  3. Question 3 Calculate 3 marks

    A car travels 120 m in 10 s at constant speed. Sketch a distance–time graph for this and calculate the gradient.

    Show answerHide answer

    Model answer

    A straight line from the origin to (10 s, 120 m). Gradient = 120 ÷ 10 = 12 m/s.

    Mark scheme

    • Straight line from the origin — 1 mark
    • Correct end point — 1 mark
    • 12 m/s — 1 mark
  4. Question 4 Explain 2 marks

    The distance–time graph for a runner is a curve that gets steeper. Describe the motion.

    Show answerHide answer

    Model answer

    The runner is accelerating (the speed is increasing).

    Mark scheme

    • Accelerating — 1 mark
    • Gradient or speed increases — 1 mark
  5. Question 5 Determine 3 marks

    The graph shows the distance of a car from a starting point against time as a curve. Describe how to find the speed at a particular time.

    Show answerHide answer

    Model answer

    Draw a tangent to the curve at that time and calculate its gradient (change in distance ÷ change in time).

    Mark scheme

    • Draw a tangent — 1 mark
    • Choose two points on the tangent — 1 mark
    • Gradient = change in distance ÷ change in time — 1 mark

Quick check

  1. The gradient of a distance–time graph is...

    1. Adistance
    2. Btime
    3. Cacceleration
    4. Dspeed
    Show answerHide answer

    D: speed

    Change in distance ÷ time.

  2. A horizontal line means...

    1. Astationary
    2. Bconstant speed
    3. Caccelerating
    4. Ddecelerating
    Show answerHide answer

    A: stationary

    Distance does not change.

  3. A steeper line means a...

    1. Aslower speed
    2. Bfaster speed
    3. Cstationary object
    4. Dzero distance
    Show answerHide answer

    B: faster speed

    Greater gradient.

  4. 80 m in 10 s gives a speed of...

    1. A800 m/s
    2. B0.125 m/s
    3. C8 m/s
    4. D90 m/s
    Show answerHide answer

    C: 8 m/s

    80 ÷ 10.

  5. A curve getting steeper shows...

    1. Aconstant speed
    2. Bbeing stationary
    3. Cdeceleration
    4. Dacceleration
    Show answerHide answer

    D: acceleration

    Speed is increasing.

Downloads

Free to keep, print and annotate.

Download all 3 as a zip
Something here looks wrong?

Tell us what and we will go and look. It goes to whoever writes these pages, nobody else, and we do not ask who you are — so there is nothing to sign and nothing comes back to you.