OCR · A-Level · Physics
Course version: H556 · Version from Sept 2015
Kinematics: (c) Displacement–time graphs; velocity is gradient
A displacement–time graph plots displacement on the vertical axis against time on the horizontal axis.
Checked against the OCR H556 specification (opens in a new tab) on .
- Point 3 of 4
- 4 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
A displacement–time graph plots displacement on the vertical axis against time on the horizontal axis. The gradient at any point equals the velocity at that time. A straight line means constant velocity; a horizontal line means zero velocity; a curve means changing velocity, so the gradient of a tangent gives the instantaneous velocity. A negative gradient means motion in the negative direction. For example, a line rising 20 m in 4 s has gradient 20 m ÷ 4 s = 5 m s⁻¹. Average velocity is the overall gradient between two points, while instantaneous velocity uses the tangent at one point.
What earns the marks
- Displacement–time graphs plot displacement against time.
- The gradient of the graph equals velocity.
- A straight line shows constant velocity and a horizontal line shows zero velocity.
- A tangent to a curve gives instantaneous velocity.
- A negative gradient indicates motion in the negative direction.
Common mistakes and how to put them right
Reading the height of the graph as velocity.
Put it right: Height is displacement; gradient is velocity.
Using two points to find instantaneous velocity on a curve.
Put it right: A tangent at the point is needed.
Ignoring the sign of the gradient.
Put it right: A negative gradient means negative velocity, not zero velocity.
Exam tips
- Draw a tangent carefully at the required point for curved graphs.
- Calculate gradient as change in displacement divided by change in time, with units.
- Check the sign of the gradient to state the direction of motion.
Try the lesson
The start of the Kinematics: (c) Displacement–time graphs; velocity is gradient lesson, made from checked teaching notes for this specification point.
Listen
A displacement–time graph plots displacement on the vertical axis against time on the horizontal axis. The gradient at any point equals the velocity at that time. A straight line means constant velocity; a horizontal line means zero velocity; a curve means changing velocity, so the gradient of a tangent gives the instantaneous velocity. A negative gradient means motion in the negative direction. For example, a line rising 20 m in 4 s has gradient 20 m ÷ 4 s = 5 m s⁻¹. Average velocity is the overall gradient between two points, while instantaneous velocity uses the tangent at one point. A strong answer earns marks for these points. Displacement–time graphs plot displacement against time. The gradient of the graph equals velocity. A straight line shows constant velocity and a horizontal line shows zero velocity. A tangent to a curve gives instantaneous velocity. Exam tip: Draw a tangent carefully at the required point for curved graphs.
See it
Key words
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Gradient as rate of change
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Constant and changing velocity
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Instantaneous versus average velocity
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Direction from sign
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See every definition
- Gradient as rate of change
- The gradient of the graph equals velocity, calculated as change in displacement divided by change in time, with units.
- Constant and changing velocity
- A straight line shows constant velocity, a horizontal line shows zero velocity, and a curve shows changing velocity.
- Instantaneous versus average velocity
- Average velocity is the overall gradient between two points, while instantaneous velocity uses the tangent at one point.
- Direction from sign
- A negative gradient indicates motion in the negative direction.
Label the diagram
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1Box 1
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3Box 3
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