Displacement & Velocity-Time Graphs (OCR A Level Physics) : Revision Note

Katie M

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Katie M

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Displacement-Time Graphs

  • Displacement-time graphs show the changing position of an object in motion

  • They also show whether an object is moving forwards (positive displacement) or backwards (negative displacement)

Velocity = Gradient of a displacement-time graph

  • The greater the slope, the greater the velocity

  • A negative gradient = a negative velocity (the object is moving backwards)

Worked Example

A car driver sees a hazard ahead and applies the brakes to bring the car to rest. What does the displacement-time graph look like?

WE - S-T gradient question image, downloadable AS & A Level Physics revision notes

Answer:

new-2-1-4-we---s-t-gradient-answer-image

Velocity-Time Graphs

  • Velocity-time graphs show the speed and direction of an object in motion over a specific period of time

  • The area under a velocity-time graph is equal to the displacement of a moving object

Displacement = Area under a velocity-time graph

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

  • 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’

Acceleration = Gradient of a velocity-time graph

Motion of a Bouncing Ball

  • For a bouncing ball, the acceleration due to gravity is always in the same direction (in a uniform gravitational field such as the Earth's surface)

    • This is assuming there are no other forces on the ball, such as air resistance

  • Since the ball changes its direction when it reaches its highest and lowest point, the direction of the velocity will change at these points

  • The vector nature of velocity means the ball will sometimes have a:

    • Positive velocity if it is travelling in the positive direction

    • Negative velocity if it is travelling in the negative direction

  • An example could be a ball bouncing from the ground back upwards and back down again

    • The positive direction is taken as upwards

    • This will be either stated in the question or can be chosen, as long as the direction is consistent throughout

  • Ignoring the effect of air resistance, the ball will reach the same height every time before bouncing from the ground again

  • When the ball is travelling upwards, it has a positive velocity which slowly decreases (decelerates) until it reaches its highest point

    Motion of Bouncing Ball 1, downloadable AS & A Level Physics revision notes
    Motion of Bouncing Ball 2, downloadable AS & A Level Physics revision notes
  • At point A (the highest point):

    • The ball is at its maximum displacement

    • The ball momentarily has zero velocity

    • The velocity changes from positive to negative as the ball changes direction

    • The acceleration, g, is still constant and directed vertically downwards

  • At point B (the lowest point):

    • The ball is at its minimum displacement (on the ground)

    • Its velocity changes instantaneously from negative to positive, but its speed (magnitude) remains the same

    • The change in direction causes a momentary acceleration (since acceleration = change in velocity / time)

Worked Example

The velocity-time graph of a vehicle travelling with uniform acceleration is shown in the diagram below.

v-t Area Worked Example (1), downloadable AS & A Level Physics revision notes

Calculate the displacement of the vehicle at 40 s.

Answer:

v-t Area Worked Example (2), downloadable AS & A Level Physics revision notes

Summary of Gradients & Areas

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

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

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

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

Motion Graphs, downloadable AS & A Level Physics revision notes

Examiner Tips and Tricks

Always check the values given on the y-axis of a motion graph - students often confuse displacement-time graphs and velocity-time graphs. The area under the graph can often be broken down into triangles, squares and rectangles, so make sure you are comfortable with calculating area!

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Katie M

Author: Katie M

Expertise: Physics Content Creator

Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.

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