Distance-time graphs

Learn it by playing

Answer these questions to earn energy, then fish and explore. No account needed.

For teachers: ready-to-use lesson slides, revision notes, diagrams for Distance-time graphs (KS3 Science, Physics) — use them in your lesson, or run the topic as an interactive class activity your students play as a live game.

Lesson notes

What is a distance-time graph?

A **distance-time graph** shows how far an object has travelled over time.
Time is plotted on the **x-axis** (horizontal) and distance on the **y-axis** (vertical).
The **gradient** (steepness) of the line represents the **speed** of the object.
A steeper gradient means a **greater speed**.

Calculating speed from the gradient

Gradient = change in distance ÷ change in time = Δy / Δx.
This is the same as the speed equation: **speed = distance ÷ time**.
Example: A jogger travels 25 m in 5 s → speed = 25 ÷ 5 = **5 m/s**.
Another jogger travels 25 m in 10 s → speed = 25 ÷ 10 = **2.5 m/s**.

Interpreting different shapes

A **straight, sloping line** indicates **constant speed**.
A **horizontal line** means the object is **stationary** (not moving).
A **curved line** shows **changing speed** (acceleration or deceleration).
If the gradient **decreases** over time, the object is **decelerating** (slowing down).
If the gradient **increases** over time, the object is **accelerating** (speeding up).

Comparing speeds on the same graph

When two lines are plotted, the **steeper line** corresponds to the **faster object**.
You can compare speeds by calculating the gradient of each line.
The line with the larger gradient has the higher speed.

Distance-time graph comparing two joggers. The steeper blue line shows a higher speed (5 m/s) than the red line (2.5 m/s).

Curved distance-time graphs: the blue curve (decreasing gradient) shows deceleration; the red curve (increasing gradient) shows acceleration.

Slides

Step through every slide for this topic — plus flashcards and revision notes — with a free account.

Practice questions

Free preview — 8 of 40 questions. Sign up to see them all.

1.What does the gradient of a distance-time graph represent?
Easy
- ASpeed
- BAcceleration
- CDistance
- DTime
2.What is the equation for speed?
Easy
- ASpeed = Distance × Time
- BSpeed = Distance ÷ Time
- CSpeed = Time ÷ Distance
- DSpeed = Distance + Time
3.A jogger runs 25 m in 5 s. What is their speed?
Medium
- A5 m/s
- B0.2 m/s
- C125 m/s
- D30 m/s
4.A jogger runs 25 m in 10 s. What is their speed?
Medium
- A2.5 m/s
- B0.4 m/s
- C250 m/s
- D15 m/s
5.In a distance-time graph, a steeper gradient indicates:
Medium
- AGreater speed
- BLower speed
- CConstant speed
- DZero speed
6.On a distance-time graph, a horizontal line indicates:
Medium
- AThe object is stationary
- BThe object is moving at constant speed
- CThe object is accelerating
- DThe object is decelerating
7.What does a decreasing gradient on a distance-time graph represent?
Medium
- ADeceleration
- BAcceleration
- CConstant speed
- DStationary object
8.What does an increasing gradient on a distance-time graph represent?
Medium
- AAcceleration
- BDeceleration
- CConstant speed
- DStationary object

More questions

9.A distance-time graph shows a straight line from (0,0) to (4,20). What is the speed?
Hard
- A5 m/s
- B0.2 m/s
- C80 m/s
- D24 m/s
10.A distance-time graph has a line that curves upwards (increasing gradient). This represents:
Hard
- AAcceleration
- BDeceleration
- CConstant speed
- DStationary
11.A distance-time graph shows a line that is straight and sloping upwards. Which statement is true?
Hard
- AThe object is moving at constant speed
- BThe object is accelerating
- CThe object is decelerating
- DThe object is stationary
12.What does the vertical axis of a distance-time graph measure?
Medium
- ADistance
- BTime
- CSpeed
- DAcceleration
13.A cyclist travels at a constant speed. Which distance-time graph represents the cyclist's motion?
Medium
- AA straight line sloping upwards from the origin
- BA horizontal line
- CA curve that becomes steeper over time
- DA straight line sloping downwards
14.A car travels 150 m in 10 s. What is its speed?
Medium
- A15 m/s
- B1500 m/s
- C0.067 m/s
- D1.5 m/s
15.A distance-time graph shows a line that starts steep and becomes less steep over time. What does this represent?
Medium
- ADeceleration
- BAcceleration
- CConstant speed
- DStationary object
16.A runner's distance-time graph shows a straight line from (0,0) to (8,40) and then a horizontal line from (8,40) to (12,40). What is the runner's speed during the first 8 seconds?
Hard
- A5 m/s
- B40 m/s
- C3.33 m/s
- D10 m/s
17.Two objects A and B have distance-time graphs. Graph A has a steeper gradient than graph B. Which statement is correct?
Hard
- AA is faster than B
- BB is faster than A
- CA has travelled further than B
- DB has travelled further than A
18.A distance-time graph shows a horizontal line. What is the object doing?
Easy
- AStationary
- BMoving at constant speed
- CAccelerating
- DDecelerating
19.A student measures the distance a toy car travels every 2 seconds. The results are: 0 s: 0 m, 2 s: 4 m, 4 s: 8 m, 6 s: 12 m. What is the speed of the car?
Medium
- A2 m/s
- B4 m/s
- C0.5 m/s
- D1 m/s
20.A distance-time graph has a curved line that gets steeper. What does this indicate about the object's motion?
Hard
- AThe object is accelerating
- BThe object is decelerating
- CThe object is moving at constant speed
- DThe object is stationary
21.A train travels 300 m in 15 s, then stops for 5 s, then travels another 200 m in 10 s. What is the total distance travelled?
Hard
- A500 m
- B300 m
- C200 m
- D600 m
22.A distance-time graph for a car shows a straight line from (0,0) to (5,100). What is the speed of the car?
Medium
- A20 m/s
- B100 m/s
- C5 m/s
- D0.05 m/s
23.A distance-time graph shows a line that goes up, then horizontal, then up again. What does this represent?
Medium
- AMoving, then stationary, then moving again
- BConstant speed throughout
- CAccelerating, then constant speed, then decelerating
- DDecelerating, then stationary, then accelerating
24.In an experiment to measure the speed of a toy car, a student records the distance travelled every 0.5 s. Which of the following is the most appropriate method to ensure accurate results?
Medium
- AUse a ruler to measure distance and a stopwatch to measure time, repeating the experiment three times and calculating the mean speed.
- BEstimate the distance by eye and use a stopwatch, taking one measurement only.
- CUse a tape measure and a stopwatch, but only record one set of readings.
- DMeasure the distance with a ruler and time with a pendulum clock.
25.A student plots a distance-time graph for a moving object. The graph shows a straight line from (0,0) to (4,20) and then a curved line that becomes less steep from (4,20) to (8,30). Which statement correctly describes the motion?
Hard
- AThe object moves at constant speed for 4 seconds, then decelerates.
- BThe object accelerates for 4 seconds, then moves at constant speed.
- CThe object moves at constant speed for 4 seconds, then accelerates.
- DThe object decelerates for 4 seconds, then moves at constant speed.
26.In an experiment to investigate motion, a student uses a ticker timer to record the position of a trolley at regular intervals. The tape produced shows dots that are evenly spaced. What does this indicate about the motion?
Medium
- AThe trolley is moving at constant speed.
- BThe trolley is accelerating.
- CThe trolley is decelerating.
- DThe trolley is stationary.
27.A car travels at a constant speed of 10 m/s for 5 seconds, then decelerates uniformly to rest over the next 5 seconds. Which distance-time graph best represents this motion?
Hard
- AA straight line from (0,0) to (5,50) followed by a curve that becomes less steep and ends horizontal at (10,75).
- BA straight line from (0,0) to (5,50) followed by a straight line with negative gradient to (10,0).
- CA curve that is steep at the start and becomes less steep from (0,0) to (10,50).
- DA straight line from (0,0) to (10,100).
28.A student measures the distance a ball rolls down a ramp every 0.2 seconds. The results are: 0.0 s: 0.0 m, 0.2 s: 0.1 m, 0.4 s: 0.4 m, 0.6 s: 0.9 m. What can be concluded about the ball's motion?
Easy
- AThe ball is accelerating.
- BThe ball is moving at constant speed.
- CThe ball is decelerating.
- DThe ball is stationary.
29.Which of the following is the correct method to calculate the speed from a distance-time graph at a specific instant?
Medium
- ADraw a tangent to the curve at that instant and calculate its gradient.
- BCalculate the gradient of the line between the start and that point.
- CMeasure the slope of the line from the origin to that point.
- DFind the area under the graph up to that time.
30.A student records the distance travelled by a toy car every second and plots a distance-time graph. The graph is a straight line from (0,0) to (5,25). The student then repeats the experiment but the car moves at half the speed. Which graph represents the second experiment?
Hard
- AA straight line from (0,0) to (5,12.5).
- BA straight line from (0,0) to (10,25).
- CA straight line from (0,0) to (2.5,25).
- DA straight line from (0,0) to (5,25) but with a dashed line.
31.In a distance-time graph, the gradient is calculated as change in distance divided by change in time. What is the unit of the gradient?
Medium
- Am/s
- Bm s
- Cs/m
- Dm/s²
32.A distance-time graph shows two lines: line A passes through (0,0) and (4,20); line B passes through (0,0) and (4,10). Which statement is correct?
Medium
- ALine A represents a speed of 5 m/s and line B represents 2.5 m/s.
- BLine A represents a speed of 20 m/s and line B represents 10 m/s.
- CLine A represents a speed of 4 m/s and line B represents 2 m/s.
- DLine A represents a speed of 0.2 m/s and line B represents 0.4 m/s.
33.On a distance-time graph, a horizontal line represents:
Easy
- AThe object is stationary.
- BThe object is moving at constant speed.
- CThe object is accelerating.
- DThe object is decelerating.
34.A student uses a motion sensor to collect data for a ball thrown vertically upwards. The distance-time graph for the ball's upward and downward journey is a curve. Which statement about the gradient of the graph at the highest point is correct?
Hard
- AThe gradient is zero, indicating the ball is momentarily stationary.
- BThe gradient is maximum, indicating the ball is moving fastest.
- CThe gradient is negative, indicating the ball is moving downwards.
- DThe gradient is positive, indicating the ball is moving upwards.
35.A student calculates the speed of a runner from a distance-time graph. The graph shows a straight line from (0,0) to (10,100). The student misreads the axes and thinks the time is on the vertical axis. What speed would they calculate?
Medium
- A0.1 m/s
- B10 m/s
- C100 m/s
- D1000 m/s
36.A distance-time graph shows a straight line from (0,0) to (6,30). What is the speed of the object?
Medium
- A5 m/s
- B6 m/s
- C30 m/s
- D0.2 m/s
37.A distance-time graph for a car shows a curve that becomes steeper over time. What does this indicate about the car's motion?
Hard
- AThe car is moving at constant speed.
- BThe car is decelerating.
- CThe car is accelerating.
- DThe car is stationary.
38.A student plots a distance-time graph for a ball rolling down a ramp. The graph is a curve that becomes less steep over time. What does this tell you about the ball's motion?
Medium
- AThe ball is accelerating.
- BThe ball is decelerating.
- CThe ball is moving at constant speed.
- DThe ball is stationary.
39.In a distance-time graph, what does a horizontal line represent?
Easy
- AConstant speed
- BAcceleration
- CDeceleration
- DStationary object
40.Two distance-time graphs are drawn on the same axes. Graph A has a steeper gradient than Graph B. What can you conclude?
Medium
- AGraph A represents a higher speed than Graph B.
- BGraph A represents a lower speed than Graph B.
- CGraph A represents a stationary object.
- DGraph A represents deceleration.

Revision notes

## Distance-Time Graphs - **Purpose**: Represent the journey of a moving object. - **Gradient (steepness)** = speed. Steeper gradient = greater speed. - **Calculating gradient**: \[ \text{gradient} = \frac{\Delta y}{\Delta x} \] For distance-time graphs, Δy = distance travelled, Δx = time taken. - **Speed equation**: \[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \] - **Examples**: - Faster jogger: 25 m in 5 s → speed = 5 m/s. - Slower jogger: 25 m in 10 s → speed = 2.5 m/s. - **Changing speed**: - **Decelerating**: gradient decreasing over time. - **Accelerating**: gradient increasing over time.

Distance-time graph: A graph showing the distance travelled by an object over time.
Gradient: The steepness of a line on a graph; for distance-time graphs, gradient = speed.
Speed: Distance travelled per unit time; calculated as distance ÷ time.
Acceleration: Increase in speed over time; shown by increasing gradient on a distance-time graph.
Deceleration: Decrease in speed over time; shown by decreasing gradient on a distance-time graph.

Flashcards

What does the gradient of a distance-time graph represent?

The gradient represents the speed of the object.

How is the gradient of a distance-time graph calculated?

Gradient = change in distance (Δy) divided by change in time (Δx).

What does a steeper gradient on a distance-time graph indicate?

A steeper gradient indicates a greater speed.

What is the equation for speed?

Speed = Distance ÷ Time.

A jogger travels 25 m in 5 s. Calculate their speed.

Speed = 25 m ÷ 5 s = 5 m/s.

A jogger travels 25 m in 10 s. Calculate their speed.

Speed = 25 m ÷ 10 s = 2.5 m/s.

What does a decreasing gradient over time on a distance-time graph indicate?

It indicates the object is decelerating (slowing down).

What does an increasing gradient over time on a distance-time graph indicate?

It indicates the object is accelerating (speeding up).

On a distance-time graph, what does a horizontal line represent?

A horizontal line represents the object is stationary (not moving).

On a distance-time graph, what does a straight diagonal line represent?

A straight diagonal line represents constant speed.

What is the symbol for change in distance?

Δy or Δd.

What is the symbol for change in time?

Δx or Δt.

What does a curved line on a distance-time graph indicate?

A curved line indicates changing speed (acceleration or deceleration).

If two objects have distance-time graphs, how can you tell which is faster?

The object with the steeper gradient (line) is faster.

What are the axes of a distance-time graph?

Distance on the y-axis (vertical) and time on the x-axis (horizontal).

What does a flat (horizontal) section on a distance-time graph mean?

The object is not moving; it is at rest.

How do you calculate speed from a distance-time graph?

Speed = gradient = (change in distance) / (change in time).

What does a straight line with positive slope on a distance-time graph show?

It shows constant speed in a straight line away from the start.

What does a straight line with negative slope on a distance-time graph show?

It shows constant speed returning towards the start (decreasing distance).

What is the speed of an object that travels 50 m in 10 s?

Speed = 50 m ÷ 10 s = 5 m/s.

What does a curve that gets steeper over time indicate?

It indicates acceleration (increasing speed).

What does a curve that gets less steep over time indicate?

It indicates deceleration (decreasing speed).

Unlock all 40 questions, flashcards & more

Create a free account to see every question, the slides, flashcards and revision notes for this topic.

Past papers

Past-paper practice for this topic is coming soon.

Coming soon