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A LevelPhysicsCIERevision Notes2. Kinematics2.1 Equations of MotionGradient of a Velocity-Time Graph

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First teaching 2023

First exams 2025

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Gradient of a Velocity-Time Graph (CIE A Level Physics)

Revision Note

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Gradient of a velocity-time graph

  • Acceleration is any change in the velocity of an object in a given time

a c c e l e r a t i o n space equals fraction numerator space c h a n g e space i n space v e l o c i t y over denominator t i m e end fraction space equals space fraction numerator open parentheses v space minus space u close parentheses space over denominator t end fraction space equals space fraction numerator increment v space over denominator increment t end fraction

  • Where:
    • v = final velocity (m s–1) 
    • u = initial velocity (m s–1) 
    • Δv = change in velocity (m s–1) 
    • Δt = change in time (s)

  • As velocity is a vector quantity, this means that if the speed of an object changes, or its direction changes, then it is accelerating
    • An object that slows down tends to be described as ‘decelerating’

  • The gradient of a velocity-time graph is equal to the acceleration

Acceleration on a velocity-time graph

velocity-time-gradient

The larger the gradient, the larger the acceleration represented on a velocity-time graph

Worked example

What does the velocity-time graph look like for this acceleration-time graph?WE - V-T gradient question image, downloadable AS & A Level Physics revision notes

Answer:

Step 1: Consider how velocity is represented on the acceleration-time graph

  • Acceleration is the gradient of a velocity-time graph

Step 2: Consider the velocity at each section of the acceleration-time graph

  • When the acceleration increases, the gradient of the velocity-time graph increases
  • When acceleration reaches a maximum, this is the maximum gradient of the velocity-time graph
  • When the acceleration decreases, the gradient of the velocity-time graph decreases

WE - V-T gradient answer image, downloadable AS & A Level Physics revision notes

Examiner Tip

A summary of the areas under the graph and gradients for the different motion graphs are:

Gradient:

  • The gradient of a displacement-time graph is the velocity
  • The gradient of a velocity-time graph is the acceleration

Area under the graph:

  • The area under a velocity-time graph is the displacement
  • The area under an acceleration-time graph is the velocity

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    Previous:Gradient of a Displacement-Time GraphNext:Deriving Kinematic Equations
    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.