Velocity-Time Graphs (AQA GCSE Physics)

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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-and-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-and-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!

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Ashika

Author: Ashika

Ashika graduated with a first-class Physics degree from Manchester University and, having worked as a software engineer, focused on Physics education, creating engaging content to help students across all levels. Now an experienced GCSE and A Level Physics and Maths tutor, Ashika helps to grow and improve our Physics resources.