OCR · A-Level · Physics
Course version: H556 · Version from Sept 2015
(d) Velocity–time graphs; acceleration is gradient; displacement is area…
Full specification wording
Kinematics: (d) Velocity–time graphs; acceleration is gradient; displacement is area under graph.
A velocity–time graph plots velocity on the vertical axis against time on the horizontal axis.
Checked against the OCR H556 specification (opens in a new tab) on .
- Point 4 of 4
Study notes
From the checked teaching notes for this specification point.
The idea
A velocity–time graph plots velocity on the vertical axis against time on the horizontal axis. The gradient of the line gives acceleration: a = Δv/Δt, so a straight line means constant acceleration, a horizontal line means zero acceleration, and a curve means changing acceleration. The area between the graph line and the time axis gives displacement; areas above the axis are positive and areas below are negative, so total displacement is the signed sum. For example, a line rising from 0 m s⁻¹ to 20 m s⁻¹ in 4 s has gradient 5 m s⁻² and area 40 m. Split complex shapes into triangles, rectangles and trapezia, and use the correct units throughout.
What earns the marks
- Gradient of a velocity–time graph equals acceleration, calculated as change in velocity divided by change in time.
- A straight line on a velocity–time graph represents constant acceleration; a horizontal line represents zero acceleration.
- Area between the graph line and the time axis represents displacement, found by splitting the region into triangles, rectangles or trapezia.
- Areas below the time axis count as negative displacement, so total displacement is the signed sum of the areas.
- Units must be consistent: velocity in m s⁻¹, time in s, acceleration in m s⁻² and displacement in m.
Common mistakes and how to put them right
Confusing the roles of gradient and area.
Put it right: Gradient gives acceleration and area gives displacement.
Ignoring the sign of areas below the time axis.
Put it right: Subtract areas below the axis when finding total displacement.
Using the wrong units or mixing them.
Put it right: Use m s⁻² for acceleration and m for displacement.
Assuming a curved velocity–time graph has constant acceleration.
Put it right: A curve means the gradient, and therefore acceleration, is changing.
Exam tips
- Read the axes and units before calculating; check whether the graph shows velocity or speed, because speed–time graphs do not show direction.
- For area, divide the region into simple shapes and label each area with its sign before adding them.
- For gradient, choose two points on the line that are far apart to reduce reading error, and show the substitution clearly.
Try the lesson
The start of the Kinematics: (d) Velocity–time graphs; acceleration is gradient; displacement is area under graph. lesson, made from checked teaching notes for this specification point.
Listen
A velocity–time graph plots velocity on the vertical axis against time on the horizontal axis. The gradient of the line gives acceleration: a = Δv/Δt, so a straight line means constant acceleration, a horizontal line means zero acceleration, and a curve means changing acceleration. The area between the graph line and the time axis gives displacement; areas above the axis are positive and areas below are negative, so total displacement is the signed sum. For example, a line rising from 0 m s⁻¹ to 20 m s⁻¹ in 4 s has gradient 5 m s⁻² and area 40 m. Split complex shapes into triangles, rectangles and trapezia, and use the correct units throughout. A strong answer earns marks for these points. Gradient of a velocity–time graph equals acceleration, calculated as change in velocity divided by change in time. A straight line on a velocity–time graph represents constant acceleration; a horizontal line represents zero acceleration. Area between the graph line and the time axis represents displacement, found by splitting the region into triangles, rectangles or trapezia. Areas below the time axis count as negative displacement, so total displacement is the signed sum of the areas. A common slip: Confusing the roles of gradient and area: the error is treating area as acceleration or gradient as displacement. Instead, gradient gives acceleration and area gives displacement. Exam tip: Read the axes and units before calculating; check whether the graph shows velocity or speed, because speed–time graphs do not show direction.
See it
Label the diagram
Some boxes have lost their names. Pick the right name for each number.
1Box 1
2Box 2
3Box 3
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