✓ Revise Right course
The gradient of a distance-time graph gives the speed: change in distance divided by change in time. Free GCSE AQA Physics notes and 14 questions answered.
Velocity, Distance-Time Graphs and Speed is part of Forces and motion in GCSE AQA Higher Physics.
5 min
Reading time
39
Lessons in this topic
GCSE AQA Higher
Pathway
Reviewed by Revise Right
Content review
The gradient of a distance-time graph gives the speed: change in distance divided by change in time. Free GCSE AQA Physics notes and 14 questions answered.
AQA GCSE Physics mock draft, 26–31 Oct. Draft coverage: Physics Paper 1 (Higher tier). Reviewed for an original-practice sitting; check student availability before registering. Marking and results will follow later, after separate approval. Eligible new accounts receive a five-day Pro trial when signup email verification completes. Previous trials keep their original expiry. After expiry, new papers need Pro unless you have an explicitly confirmed free sitting offer for this event. That offer adds no Pro time or AI learning. Saved attempts and released results remain readable. No card or automatic charge.
Use this lesson to stay inside Forces and motion while connecting the detail back to the wider Forces topic.
Read the core explanations from Velocity, Distance-Time Graphs and Speed before testing yourself from memory.
Picture a car driving around a circular track at exactly 60 mph. The speedometer never changes, yet the car is constantly accelerating. This seems impossible until you understand the crucial difference between speed and velocity.
Speed tells you how fast something is moving. It's a scalar quantity - just a number with units. When you say "the car travels at 30 m/s", that's speed.
Velocity includes direction. It's a vector quantity. The same car travelling at 30 m/s north has a different velocity from one travelling at 30 m/s east, even though their speeds are identical.
Here's where it gets interesting for circular motion. An object moving in a circle at constant speed has changing velocity because its direction constantly changes. The speed stays the same, but velocity is always changing direction.
Distance-time graphs tell the story of motion. The x-axis shows time, the y-axis shows total distance travelled. Every point on the line represents where the object was at that moment.
A horizontal line means the object isn't moving - distance stays the same as time passes. A straight diagonal line means constant speed - the object covers equal distances in equal time intervals.
A curved line reveals changing speed. If the curve gets steeper, the object is speeding up. If it gets less steep, the object is slowing down. The steepness at any point tells you the instantaneous speed.
Reading these graphs becomes second nature once you remember: steep means fast, gentle means slow, horizontal means stopped. The gradient is everything - it's the mathematical way to extract speed from the graph.
The gradient of a distance-time graph gives you speed. This isn't just a mathematical trick - it's the fundamental definition of speed as rate of change of distance with time.
For a straight line, gradient equals rise over run: change in distance divided by change in time. This gives you the average speed over that time period.
For curved lines, you need the gradient at a specific point. This requires drawing a tangent - a straight line that just touches the curve at that point. The gradient of the tangent gives the instantaneous speed.
Worked example: Calculating Speed from a Distance-Time Graph
A car travels from 0m to 120m in the first 8 seconds, then stays at 120m for 4 seconds. Calculate the speed in each section.
Answer: First section: 15 m/s, Second section: 0 m/s (stationary)
When objects accelerate, their distance-time graphs become curved. The speed is constantly changing, so we need a way to find the speed at any specific moment - the instantaneous speed.
Drawing a tangent to the curve at the point of interest gives us this instantaneous speed. The tangent line represents what the motion would look like if the object continued at that exact speed from that moment.
To draw an accurate tangent, place your ruler so it just touches the curve at one point without crossing it. The line should have the same direction as the curve at that exact point.
Worked example: Finding Instantaneous Speed Using Tangents
A ball's distance-time graph shows a curve. At t = 3s, draw a tangent and find the instantaneous speed if the tangent passes through (2s, 10m) and (4s, 30m).
Answer: Instantaneous speed at t = 3s is 10 m/s
This tangent method is crucial for Higher Tier students. It bridges the gap between average speed (straight line gradient) and instantaneous speed (tangent gradient) for accelerating objects.
Creating accurate distance-time graphs from data requires careful plotting and understanding of what each section represents. Start by identifying the scale that best fits your data range.
Plot each data point carefully, then decide whether to connect with straight lines or smooth curves. Straight lines indicate constant speed between measurements, while curves suggest continuous acceleration.
When interpreting graphs, look for patterns: horizontal sections (stationary), straight diagonal sections (constant speed), and curved sections (changing speed). The steepness always indicates how fast the object is moving.
Common mistakes include confusing distance-time graphs with speed-time graphs, or thinking that a curved line means the object is following a curved path. Remember: the graph shows distance against time, not the actual route taken.
Distance-time graph questions are mark-rich opportunities in GCSE Physics. Examiners test your ability to extract information, perform calculations, and avoid common misconceptions.
When calculating speed from gradients, always show your triangle clearly on the graph. Mark the coordinates you're using and include units in your final answer. Examiners award method marks for correct approach even if your arithmetic is wrong.
Many students confuse distance-time graphs with displacement-time or speed-time graphs. Distance-time graphs always show cumulative distance travelled, never negative values, and the gradient gives speed, not acceleration.
For Higher Tier tangent questions, draw your tangent line clearly and extend it far enough to read coordinates accurately. Use a sharp pencil and ruler - sketchy tangents lose marks.
Published by Revise Right. Use the official specification reference to check the requirements for your course. Content updated: 2026-03-20.
Move to the related lessons or back to the topic page when you need the wider sequence before exam-style practice.
Velocity can be positive or negative depending on the chosen direction, because it is the rate of change of displacement in a specific direction. Speed, however, is always positive.
The gradient of a distance-time graph gives the speed: change in distance divided by change in time. A car travelling from 0m to 120m in 8 seconds has a gradient, and so a speed, of 120 ÷ 8 = 15 m/s.
A horizontal line on a distance-time graph means the object is not moving, because distance stays the same as time passes. A straight diagonal line means constant speed, and a curved line means changing speed.
Draw a tangent that just touches the curve at the point of interest, then find its gradient. A tangent at t = 3s through (2s, 10m) and (4s, 30m) has a gradient of 20 ÷ 2 = 10 m/s, the instantaneous speed.
Velocity can change at constant speed because velocity includes direction. An object moving in a circle at constant speed has changing velocity because its direction constantly changes, so a car on a circular track is constantly accelerating.
A curved line on a distance-time graph shows changing speed: if the curve gets steeper the object is speeding up, and if it gets less steep the object is slowing down. It does not mean the object is following a curved path.
A straight diagonal line on a distance-time graph means constant speed: the object covers equal distances in equal time intervals. The steeper the line, the faster the speed.
A tangent is drawn by placing a ruler so it just touches the curve at one point without crossing it, with the same direction as the curve at that point. It should be drawn clearly with a sharp pencil and extended far enough to read coordinates accurately.
A car that travels from 0 m to 120 m in 8 s has a speed of 120 ÷ 8 = 15 m/s. If the graph then stays at 120 m for 4 s, the speed in that section is 0 m/s, because the car is stationary.
A tangent through (2 s, 10 m) and (4 s, 30 m) has a gradient of (30 − 10) ÷ (4 − 2) = 20 ÷ 2 = 10 m/s. This gradient is the instantaneous speed at the point where the tangent touches the curve.
A car going round a circular track at constant speed is constantly accelerating, because its direction keeps changing. The speed stays the same, but its velocity, which includes direction, is always changing.
Average speed is the gradient of a straight line between two points on a distance-time graph, while instantaneous speed is the gradient of a tangent at one point on a curve. The tangent shows the speed at that exact moment.
To plot a distance-time graph, a scale that fits the data range is picked, each point is plotted carefully, and the points are connected with straight lines for constant speed or a smooth curve for continuous acceleration. Time goes on the x-axis and distance on the y-axis.
On a distance-time graph the gradient gives speed, and the line shows cumulative distance travelled, never negative values. Confusing distance-time graphs with displacement-time or speed-time graphs is a common mistake.