Section 1 of 7Reading a distance-time graph
What the graph shows
- What the graph shows Time is plotted on the horizontal axis and the distance from the starting point on the vertical axis.
- The line tells you where the object is at every moment of the journey.
Straight sloping line
- Straight sloping line A straight line means the object covers equal distances in equal times, so it is moving at a constant speed.
- The steeper the line, the faster the object is going.
Horizontal line
- Horizontal line The distance is not changing, so the object is stationary.
Curved line
- Curved line A curve means the gradient is changing, so the speed is changing.
- A line getting steeper shows the object speeding up; a line levelling off shows it slowing down.
Section 2 of 7Finding speed from the gradient
1
Choose a straight section of the line and draw a large right-angled triangle under it, so that reading errors are small.
2
Read the change in distance (Δy) from the vertical side and the change in time (Δx) from the horizontal side.
3
Convert to standard units if needed: kilometres to metres (× 1000) and minutes to seconds (× 60).
4
Use speed = gradient = Δy ÷ Δx = distance ÷ time.
5
Worked example: a train travels 8 km in 6 minutes at constant speed. That is 8000 m in 360 s, so speed = 8000 ÷ 360 = 22.2 m/s.
Section 3 of 7Interpreting a journey
| Section of graph | Shape of line | What the object is doing |
|---|---|---|
| Section A | Straight, sloping upwards | Walking away at a steady speed |
| Section B | Horizontal | Stopped (for example, sitting on a bench for 40 minutes) |
| Section C | Straight, steeper than A | Moving faster than before (for example, running home) |
| End of the line | Final point on the distance axis | Read off the total distance travelled, for example 0.6 km |
Section 4 of 7Velocity-time graphs
Velocity against time
Gradient is acceleration
- Gradient is acceleration The gradient of a velocity-time graph equals the acceleration: a = Δv ÷ Δt, measured in m/s2.What the symbols mean: a = acceleration (m s−2) · v = final velocity · u = initial velocity (m s−1) · Δv = change in velocity · t = time taken (s)
- A steep line means a large acceleration or deceleration; a gentle slope means a small one.
Straight sloping line
- Straight sloping line The acceleration is constant.
- A line sloping upwards is speeding up;
- a line sloping downwards is slowing down (deceleration).
- A line sloping upwards is speeding up;
Horizontal line
- Horizontal line The velocity is constant, so the acceleration is zero.
- The object is not necessarily stopped, because it may be moving steadily.
Worked example
- Worked example A cyclist's velocity rises from 4 m/s to 10 m/s between 5 s and 10 s.
- Acceleration = (10 − 4) ÷ (10 − 5) = 6 ÷ 5 = 1.2 m/s2.
Section 5 of 7Comparing the two graphs
| Feature | Distance-time graph | Velocity-time graph |
|---|---|---|
| Gradient means | Speed | Acceleration |
| Horizontal line means | Stationary | Constant velocity |
| Straight sloping line | Constant speed | Constant acceleration |
| Curved line | Changing speed | Changing acceleration |
Section 6 of 7Key terms
| Term | Meaning |
|---|---|
| Gradient | How steep a line is, found by dividing the change in the vertical value by the change in the horizontal value. |
| Stationary | Not moving; the distance from the start stays the same. |
| Constant speed | Covering equal distances in equal intervals of time. |
| Acceleration | The rate of change of velocity, measured in metres per second squared. |
| Deceleration | A negative acceleration, where an object slows down. |
| Gradient triangle | A right-angled triangle drawn on a graph to measure the change in y and the change in x. |
Section 7 of 7Exam technique
1
Reading a horizontal line on a distance-time graph as constant speed — it means the object has stopped.
2
Reading a horizontal line on a velocity-time graph as stationary — it means constant velocity, and the acceleration is zero.
3
Using a tiny gradient triangle, which makes the answer inaccurate; draw the triangle as large as the line allows.
4
Forgetting to convert minutes and kilometres into seconds and metres before calculating speed in m/s.
5
Confusing the two gradientsthe gradient of a distance-time graph is speed, but on a velocity-time graph it is acceleration.
Marked practiceQuizzes for this lesson
Physics 0625 & 9702 SUVAT Mastery
Graph Interpretation
Constant Acceleration Equations (SUVAT) & Slopes
v = u + at | s = ut + ½at2 | v2 = u2 + 2as | s = ½(u + v)t
- Displacement-Time Graph: Gradient = Velocity (curve = accelerating).
- Velocity-Time Graph: Gradient = Acceleration; Area under curve = Distance travelled / Displacement.
- Free Fall in vacuum:
a = g ≈ 9.81 m/s2downwards (air resistance negligible).