Velocity-Time Graphs (Edexcel GCSE Physics: Combined Science)

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Velocity-Time Graphs

  • 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

Gradient of a Velocity-Time Graph

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

acceleration space equals space gradient space equals space fraction numerator increment x over denominator increment y end fraction

velocity-time-gradient

The gradient of a velocity-time graph can be found by dividing the change in velocity by the change in time

Worked example

A cyclist is training for a cycling tournament.

The velocity-time graph below shows the cyclist's motion as they cycle 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 the cyclist's acceleration the largest?

(b) Calculate the cyclist's acceleration between 5 and 10 seconds.

 

Answer:

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 the cyclist is accelerating are sections B and D

  • Sections A, C, and E are flat; in other words, the cyclist is moving at a constant velocity (therefore, 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 

velocity-time-graph-we

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:

a space equals space fraction numerator increment y over denominator increment x end fraction

a space equals space 5 over 5

a space equals space 1 space straight m divided by straight s squared

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

Examiner Tip

Use the entire slope, where possible, to calculate the gradient. Examiners tend to award credit if they see a large gradient triangle used.

Remember to actually draw the lines directly on the graph itself, particularly when the question asks you to use the graph to calculate the acceleration. 

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Ashika

Author: Ashika

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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.