AQA GCSE Physics

Revision Notes

5.6.11 Velocity-Time Graphs

Gradient of a Velocity-Time Graph

  • A velocity-time graph shows how the velocity of a moving object varies with time
    • The red line represents an object with increasing velocity
    • The green line represents an object with decreasing velocity

Velocity-Time Graph, downloadable IGCSE & GCSE Physics revision notes

Increasing and decreasing velocity represented on a velocity-time graph

Acceleration on a Velocity-Time Graph

  • Velocity-time graphs also show the following information:
    • If the object is moving with a constant acceleration/deceleration
    • The magnitude of the acceleration/deceleration
  • A straight line represents constant acceleration
  • The slope of the line represents the magnitude of acceleration
    • A steep slope means large acceleration (or deceleration) – i.e. the object’s speed changes very quickly
    • A gentle slope means small acceleration (or deceleration) – i.e. the object’s speed changes very gradually
    • A flat line means the acceleration is zero – i.e. the object is moving with a constant velocity

velocity-time-graphs, IGCSE & GCSE Chemistry revision notes

Interpreting the slope of a velocity-time graph

Calculating the Gradient of a Velocity-Time Graph

  • The acceleration of an object can be calculated from the gradient of a velocity-time graph

Velocity-Time Gradient, downloadable IGCSE & GCSE Physics revision notes

The gradient of a velocity-time graph

Worked Example

Tora is training for a cycling tournament.
The velocity-time graph below shows her motion as she cycles along a flat, straight road.

WE V-T graph Question image, downloadable IGCSE & GCSE Physics revision notes
(a) In which section (A, B, C, D, or E) of the velocity-time graph is Tora’s acceleration the largest?
(b) Calculate Tora’s acceleration between 5 and 10 seconds.

Part (a)

Step 1: Recall that the slope of a velocity-time graph represents the magnitude of acceleration

    • The slope of a velocity-time graph indicates the magnitude of acceleration
      Therefore, the only sections of the graph where Tora is accelerating is section B and section D
    • Sections A, C, and E are flat – in other words, Tora is moving at a constant velocity (i.e. not accelerating)

Step 2: Identify the section with the steepest slope

    • Section D of the graph has the steepest slope
      Hence, the largest acceleration is shown in section D

Part (b)

Step 1: Recall that the gradient of a velocity-time graph gives the acceleration

    • Calculating the gradient of a slope on a velocity-time graph gives the acceleration for that time period

Step 2: Draw a large gradient triangle at the appropriate section of the graph

    • A gradient triangle is drawn for the time period between 5 and 10 seconds below:

WE V-T graph Solution image, downloadable IGCSE & GCSE Physics revision notes

Step 3: Calculate the size of the gradient and state this as the acceleration

    • The acceleration is given by the gradient, which can be calculated using:

acceleration = gradient = 5 ÷ 5 = 1 m/s2

    • Therefore, Tora accelerated at 1 m/s2 between 5 and 10 seconds

Exam Tip

Use the entire line, where possible, to calculate the gradient. Examiners tend to award credit if they see a large gradient triangle used – so remember to draw ‘rise’ and ‘run’ lines directly on the graph itself!

Author: Jonathan

Jonathan graduated with a first-class Master's degree in Theoretical Physics from Imperial College London. He has worked in education for more than a decade as a Maths and Physics Teacher, Tutor, Head of Physics, and most recently, as Assistant Headteacher. He is now an Educational Consultant and works with us to design and improve our Physics resources.
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