A picture is worth a thousand words — and in physics, a graph is worth a thousand measurements. Motion graphs let us see speed, acceleration and distance at a glance, turning numbers into stories about how objects move.
Look at this simple distance-time graph in your mind: a straight line going up from left to right.
Write down your answers before reading on:
Reading the story of motion from a simple graph
A distance-time graph shows how the distance travelled by an object changes over time.
The gradient (slope) of a distance-time graph gives the speed:
Speed = change in distance / change in time
Understanding how speed changes over time
A speed-time graph shows how the speed of an object changes over time.
The gradient of a speed-time graph gives the acceleration:
Acceleration = change in speed / change in time
Finding distance from speed-time graphs
The area under a speed-time graph represents the total distance travelled by the object.
For simple shapes:
This is a powerful tool — even if the speed changes irregularly, the area under the curve still gives the total distance.
Using graphs to compare different objects
Motion graphs let us compare different objects visually:
Example: In a race between a sprinter and a marathon runner, the sprinter's distance-time graph starts very steep (fast) but flattens out quickly (tires). The marathon runner's graph is less steep but stays steady for much longer.
"A horizontal line on a distance-time graph means the object is moving at constant speed." No — a horizontal line means the object is stationary (not moving). A straight line sloping upward means constant speed.
"Acceleration always means speeding up." No — acceleration is the rate of change of speed. Negative acceleration (deceleration) means slowing down.
Formula 1 and motorsport: Australia hosts the Australian Grand Prix in Melbourne. Engineers use speed-time and distance-time graphs to analyse car performance, optimise braking points and compare lap times. Tiny differences in acceleration shown on graphs can separate first place from tenth.
Traffic management: Australian transport authorities use motion data from GPS and sensors to analyse traffic flow. Graphs of speed versus time help identify congestion points and design better road networks. Smart motorways in Sydney and Melbourne use real-time motion analysis to adjust speed limits.
Athletics coaching: Australian Institute of Sport scientists use motion graphs to analyse sprinters' acceleration patterns. Graphs showing speed over time reveal whether an athlete is reaching peak speed too early or too late in a race, allowing coaches to adjust training programs.
1. What does the slope of a distance-time graph represent?
2. A horizontal line on a speed-time graph means:
3. What does the area under a speed-time graph represent?
4. An object speeds up from 0 to 20 m/s in 5 seconds. What is its acceleration?
5. On a distance-time graph, a steeper line indicates:
1. Describe the motion shown by each section of a distance-time graph that: (a) is horizontal, (b) slopes upward steadily, (c) curves upward becoming steeper. 4 MARKS
2. A car travels at 15 m/s for 10 seconds, then accelerates uniformly to 25 m/s over the next 5 seconds. Draw a speed-time graph and calculate the total distance travelled. 4 MARKS
3. Explain how you can tell from a distance-time graph which of two objects is moving faster, and how you can tell from a speed-time graph which object has greater acceleration. 4 MARKS
Go back to your Think First answer. Has your understanding changed?
C — The slope (gradient) of a distance-time graph represents speed. Steeper slope = higher speed.
B — A horizontal line on a speed-time graph means constant speed because the speed is not changing over time. Zero acceleration.
B — The area under a speed-time graph represents the total distance travelled by the object.
B — Acceleration = change in speed / change in time = (20 - 0) / 5 = 4 m/s².
B — On a distance-time graph, a steeper line means the object covers more distance in the same time, which means greater speed.
Model answer: (a) A horizontal line on a distance-time graph means the object is stationary — its distance is not changing over time. (b) A straight line sloping upward steadily means the object is moving at constant speed — the distance increases by the same amount each second. (c) A line that curves upward becoming steeper means the object is speeding up — it covers more distance each second, so its speed is increasing.
Model answer: The speed-time graph shows a horizontal line at 15 m/s from 0 to 10 seconds, then a straight line rising from 15 m/s to 25 m/s from 10 to 15 seconds. Distance = area under graph = (10 x 15) + 1/2 x 5 x (15 + 25) = 150 + 100 = 250 metres.
Model answer: On a distance-time graph, the object with the steeper slope is moving faster because it covers more distance in the same time. Speed equals the gradient of the distance-time graph. On a speed-time graph, the object with the steeper positive slope has greater acceleration because its speed is increasing more rapidly. Acceleration equals the gradient of the speed-time graph.
Race against time to interpret motion graphs! Match descriptions to graphs, calculate speeds and predict motion in this fast-paced challenge.
Tick when you have finished all activities and checked your answers.