- 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.
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.
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.
- 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
The object is stationary — distance is not changing as time passes.
(22 − 10) ÷ 6 = 12 ÷ 6 = 2 m/s².
Yes — its direction is changing, so its velocity is changing, which means it is accelerating even though its speed is constant.
100 ÷ 12.5 = 8 m/s.
Quick check
Which of these best defines "speed"?
A car travels at a steady 25 m/s for 40 s. How far does it go?
- 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