AQA · GCSE · Physics

    Course version: 8463 · Version from Sept 2016

    The acceleration of an object can be calculated from the gradient of a…

    Full specification wording

    Acceleration: The acceleration of an object can be calculated from the gradient of a velocity–time graph.

    On a velocity-time graph the vertical axis is velocity and the horizontal is time, so the gradient is a change in velocity divided by a time, which is the definition of acceleration.

    Checked against the AQA 8463 specification (opens in a new tab) on .

    • Point 16 of 23
    • 4 key terms

    Study notes

    From the checked teaching notes for this specification point.

    The idea

    On a velocity-time graph the vertical axis is velocity and the horizontal is time, so the gradient is a change in velocity divided by a time, which is the definition of acceleration. A horizontal line means constant velocity and zero acceleration; a straight sloping line means constant acceleration; a line sloping downwards means the object is slowing, and the gradient comes out negative. Take the gradient from a large triangle: a velocity rising from 4 m/s to 20 m/s over 8.0 s gives an acceleration of 2.0 m/s². Where the line curves the acceleration is changing, so a tangent is needed to find its value at a particular instant. Do not confuse this graph with a distance-time graph, on which the gradient is a speed.

    What earns the marks

    • Identifying the gradient of the velocity-time line as the acceleration.
    • Reading a change in velocity with its matching change in time from a large triangle.
    • The substitution and the calculated value.
    • The unit metres per second squared, negative where the line slopes downwards.

    Common mistakes and how to put them right

    • Reading the velocity at a point and calling it the acceleration.

    • Treating a horizontal line as zero velocity rather than zero acceleration.

    • Ignoring the negative sign when the line slopes downwards.

    • Using the area under the line when the gradient was asked for.

    Exam tips

    • Say which graph you are looking at first, because the gradient means different things on the two.
    • Use grid intersections for your triangle so that both readings are exact.

    Try the lesson

    The start of the Acceleration: The acceleration of an object can be calculated from the gradient of a velocity–time graph. lesson, made from checked teaching notes for this specification point.

    Have a go first

    How can the acceleration of an object be determined directly from a velocity–time graph?

    Listen

    On a velocity-time graph the vertical axis is velocity and the horizontal is time, so the gradient is a change in velocity divided by a time, which is the definition of acceleration. A horizontal line means constant velocity and zero acceleration; a straight sloping line means constant acceleration; a line sloping downwards means the object is slowing, and the gradient comes out negative. Take the gradient from a large triangle: a velocity rising from 4 m/s to 20 m/s over 8.0 s gives an acceleration of 2.0 m/s². Where the line curves the acceleration is changing, so a tangent is needed to find its value at a particular instant. Do not confuse this graph with a distance-time graph, on which the gradient is a speed. A strong answer earns marks for these points. identifying the gradient of the velocity-time line as the acceleration. reading a change in velocity with its matching change in time from a large triangle. the substitution and the calculated value. the unit metres per second squared, negative where the line slopes downwards. Exam tip: Say which graph you are looking at first, because the gradient means different things on the two.

    See it

    A top-down flowchart. The top node reads "Velocity–time graph". An arrow leads down to "Gradient = change in velocity ÷ time", which leads down to "Gradient = acceleration". From the top node, four further arrows lead to separate branches. The first branch goes to "Horizontal line" and then to "Constant velocity, zero acceleration". The second goes to "Straight sloping line" and then to "Constant acceleration". The third goes to "Line sloping downwards" and then to "Object slowing, negative gradient". The fourth goes to "Curved line" and then to "Acceleration changing, tangent needed".
    It shows that the gradient of a velocity–time graph is the acceleration, and what horizontal, rising, falling and curved lines each mean.

    Key words

    Say what each word means before you turn the card.

    velocity-time graph

    Try answering aloud or in your head before turning the card.

    gradient as acceleration

    Try answering aloud or in your head before turning the card.

    negative gradient

    Try answering aloud or in your head before turning the card.

    large triangle

    Try answering aloud or in your head before turning the card.

    See every definition
    velocity-time graph
    A graph on which the vertical axis is velocity and the horizontal is time, so the gradient is a change in velocity divided by a time.
    gradient as acceleration
    The gradient of a velocity-time line is the acceleration, found by reading a change in velocity with its matching change in time from a large triangle.
    negative gradient
    A line sloping downwards means the object is slowing, and the gradient comes out negative.
    large triangle
    A triangle used to take the gradient, with both readings exact from grid intersections, such as a velocity rising from 4 m/s to 20 m/s over 8.0 s.

    Label the diagram

    Some boxes have lost their names. Pick the right name for each number.

    The diagram again, with 3 boxes numbered instead of named. A top-down flowchart. The top node reads "Velocity–time graph". An arrow leads down to "Gradient = change in velocity ÷ time", which leads down to "Gradient = acceleration". From the top node, four further arrows lead to separate branches. The first branch goes to "Horizontal line" and then to "Constant velocity, zero acceleration". The second goes to "Straight sloping line" and then to "Constant acceleration". The third goes to "Line sloping downwards" and then to "Object slowing, negative gradient". The fourth goes to "Curved line" and then to "Acceleration changing, tangent needed".

    • 1Box 1

    • 2Box 2

    • 3Box 3

    0 of 3 labelled

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