Displacement, Velocity & Acceleration (CIE A Level Physics)

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

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

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:

• 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  of an object can be calculated using

• Where:
  • = total displacement, or change in position, measured in (m)
  • = 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:

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:

• Where:
  • = average acceleration, measured in m s^–2
  • = change in velocity, measured in m s^–1
  • = 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