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Physics
Distance-Time & Velocity-Time Graphs
Motion Graphs
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Distance time and velocity time graphs are two powerful ways to describe motion. They let you turn a real event, such as a cyclist speeding up or a car stopping at a red light, into a picture that can be measured. The shape and steepness of a graph show whether an object is still, moving steadily, speeding up, or slowing down. Learning to read these graphs helps students connect everyday motion to scientific models.
Key Facts
- Speed = distance ÷ time, so v = d/t.
- On a distance time graph, the gradient equals speed.
- A horizontal line on a distance time graph means the object is stationary.
- On a velocity time graph, the gradient equals acceleration, so a = Δv/Δt.
- The area under a velocity time graph equals distance traveled.
- A horizontal line on a velocity time graph means constant velocity, not rest unless velocity is 0.
Vocabulary
- Distance
- Distance is the total length of the path traveled by an object.
- Velocity
- Velocity is speed in a specific direction.
- Gradient
- Gradient is the steepness of a graph and is found by rise divided by run.
- Acceleration
- Acceleration is the rate at which velocity changes over time.
- Stationary
- Stationary means not moving, so the position or distance from the start is not changing.
Common Mistakes to Avoid
- Calling a flat distance time graph constant speed. This is wrong because the distance is not changing, so the object is stationary.
- Thinking a steeper line always means more acceleration. On a distance time graph, steepness shows speed, while on a velocity time graph, steepness shows acceleration.
- Reading the height of a velocity time graph as distance. This is wrong because the height gives velocity, and distance comes from the area under the graph.
- Forgetting units on graph axes and answers. This is wrong because time, distance, velocity, and acceleration need correct units such as s, m, m/s, and m/s².
Practice Questions
- 1 A student walks 60 m in 20 s at a constant speed. What is the speed, and what would the gradient of the distance time graph be?
- 2 A cyclist increases velocity from 2 m/s to 10 m/s in 4 s. What is the acceleration shown by the gradient of the velocity time graph?
- 3 A distance time graph rises in a straight line, then becomes horizontal, then rises again with a steeper straight line. Describe the motion during each section.