Velocity–Time Graphs

Finding acceleration from the gradient and distance from the area under the graph.

  • Define and explain Velocity–Time Graphs in your own words
  • Use key terms such as speed accurately
  • Apply what you have learned to new examples and questions
  • Avoid the common mistakes learners make with this topic

This lesson focuses on Velocity–Time Graphs: finding acceleration from the gradient and distance from the area under the graph.

Definition: Velocity–Time Graphs

Finding acceleration from the gradient and distance from the area under the graph.

Key ideas

Graphs turn journeys into pictures

On a distance–time graph, the gradient (slope) equals the speed — steeper means faster, flat means stationary. On a velocity–time graph the gradient gives acceleration, and the area under the line gives the distance travelled. One graph can replace a whole table of data.

Speed tells you how fast, velocity tells you how fast and where to

Speed = distance ÷ time is a scalar with no direction. Velocity adds direction, making it a vector. Two cars can share a speed of 20 m/s yet have different velocities if they head opposite ways — and that difference matters in collisions.

Key term — speed: How fast something moves: distance travelled divided by time taken, measured in m/s or km/h.

Worked example: Velocity–Time Graphs

How is distance found from a velocity–time graph?

It equals the area under the graph, between the line and the time axis.

Answer: It equals the area under the graph, between the line and the time axis.

Common mistakes
  • Reading the gradient of a velocity–time graph as speed The gradient of a velocity–time graph is acceleration; speed is read straight off the vertical axis.
  • Mixing up distance and displacement Distance is the total path travelled; displacement is the straight line from start to end — they match only on a straight one-way trip.

Practice

On a distance–time graph, what does a flat horizontal section mean?
Is the distance changing?

The object is stationary — distance is not changing as time passes.

A van accelerates from 10 m/s to 22 m/s in 6 s. Find the acceleration.
a = (v − u) ÷ t.

(22 − 10) ÷ 6 = 12 ÷ 6 = 2 m/s².

A train rounds a bend at a constant 40 m/s. Is it accelerating? Explain.
Velocity includes direction.

Yes — its direction is changing, so its velocity is changing, which means it is accelerating even though its speed is constant.

A runner covers 100 m in 12.5 s. Calculate the average speed.
Divide distance by time.

100 ÷ 12.5 = 8 m/s.

Quick check

Velocity–Time Graphs — quick check

Which of these best defines "speed"?

How fast something moves: distance travelled divided by time taken, measured in m/s or km/h.

A car travels at a steady 25 m/s for 40 s. How far does it go?

25 × 40 = 1000 m.
Key takeaways
  • Velocity–Time Graphs: finding acceleration from the gradient and distance from the area under the graph.
  • Graphs turn journeys into pictures: On a distance–time graph, the gradient (slope) equals the speed — steeper means faster, flat means stationary.
  • acceleration: The rate of change of velocity, in m/s².
  • Watch out for: reading the gradient of a velocity–time graph as speed