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Displacement, Velocity & Acceleration (CIE AS Physics)

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Defining displacement, velocity & acceleration

Distance and displacement

Distance

  • Distance is a measure of how far an object travels
  • It is a scalar quantity with magnitude only

Total running distance

300 m Race Distance, downloadable IGCSE & GCSE Physics revision notes

The athletes run a total distance of 300 m

  • Consider some athletes running a 300 m race on a 400 m track
  • The distance travelled by the athletes is 300 m

Displacement

  • Displacement is a measure of how far something is from its starting position, along with its direction
    • In other words, it is the change in position
  • It is a vector quantity with both magnitude and direction

Total distance vs total displacement

300 m Race Displacement, downloadable IGCSE & GCSE Physics revision notes

The athletes run a total distance of 300 m, but end up 100 m from where they started

  • Consider the same 300 m race again
    • The athletes have still run a total distance of 300 m (this is indicated by the arrow in red)
    • However, their displacement at the end of the race is 100 m to the right (this is indicated by the arrow in green)
    • If they had run the full 400 m, their final displacement would be zero
  • Distance is a scalar quantity because...

It describes how far an object has travelled overall, but not the direction it has travelled in

  • Displacement is a vector quantity because...

It describes how far an object is from where it started and in what direction

Speed and velocity

Speed

  • The speed of an object is the distance it travels every second
  • Speed is a scalar quantity with magnitude only

    • The average speed of an object is given by the equation:

    average space speed space equals space fraction numerator space total space distance over denominator time space taken end fraction

    • The SI units for speed are meters per second (m s−1) but speed can often be measured in alternative units e.g. km h−1 or mph, when it is more appropriate for the situation

    Velocity

    • The velocity of a moving object is similar to its speed and also describes the direction of the velocity
    • Velocity is defined as:

    The rate of change of displacement

    • Velocity is, therefore, a vector quantity because it describes both magnitude and direction
    • Velocity is the speed in a given direction
    • The average velocity v subscript a v g end subscript of an object can be calculated using

    v subscript a v g end subscript space equals space fraction numerator increment x over denominator increment t end fraction

    • Where:
      • increment x = total displacement, or change in position, measured in (m)
      • increment t = total time taken, measured in (s)
    • If the initial velocity u and final velocity v are known, the average velocity can also be calculated using:

    v subscript a v g end subscript space equals space fraction numerator open parentheses u space plus space v close parentheses over denominator 2 end fraction

    Examiner Tip

    Velocity is speed in a given direction, but average velocity is not average speed in a given direction. This is because speed uses distance, and velocity uses displacement, and the magnitudes of these values can be very different for the same motion. 

    Acceleration

    • Acceleration is defined as:

    The rate of change of velocity

    • Acceleration is a vector quantity and is measured in metres per second squared (m s–2)
      • It describes how much an object's velocity changes every second
    • The average acceleration of an object can be calculated using:

    average space acceleration space equals space fraction numerator change space in space velocity space over denominator time space taken end fraction

    a space equals space fraction numerator increment v over denominator increment t end fraction

    • Where:
      • a = average acceleration, measured in m s–2
      • increment v = change in velocity, measured in m s–1
      • increment t = total time taken, measured in s
    • The change in velocity is the difference between the initial and final velocity, as written below:

    change in velocity = final velocity − initial velocity

    increment v space equals space open parentheses v space minus space u close parentheses

    Worked example

    A professor walks around her garden following the path ABCDA. 

    1-1-1-distance-and-displacement-we

    Calculate, at the end of their walk

    (a)
    the distance the professor travels.
    (b)
    the displacement of the professor.
     

    Answer:

    (a) The distance the professor travels is:

    • The total distance of each side of the rectangle

    15 + 9 + 15 + 9 = 48 km

    (b) The displacement of the professor is:

    • The displacement is how far the professor is from their original position
    • As they travel back to point A, the total displacement = 0 km

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    Ashika

    Author: Ashika

    Expertise: Physics Project Lead

    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.