Displacement, Speed and Velocity


Distance and Displacement

Distance and displacement are both ways of describing how far an object has travelled. The difference is that distance is a scalar quantity and displacement is a vector quantity.

Visually, as seen below, distance (s) can be considered the length that the object has travelled along the path it travelled – this may involve turns, bends, going backwards and forwards again. Displacement (\overset { \rightarrow }{ s } ) can be seen as the length between the starting and finishing points irrespective of the path taken. Displacement must take into account the direction. The 

In one dimension, or straight line motion, displacement can be considered the length from the origin to the finishing point, where one direction is positive and the other is negative.

In the example below, if O is the origin, we can say that A is 4 units from the origin and B is -2 units from the origin (units could be m or km, or some other unit for length). We could also say that A is 6 units from B and B is -6 units from A.


Speed and Velocity

Speed and velocity are both ways of describing how fast an object is moving. The difference is that speed is a scalar quantity and velocity is a vector quantity.

Speed, (v) is the rate at which distance changes as time changes. It can be found by dividing the distance travelled by the time taken. The unit for speed is m/s or ms-1. The equation for speed is:

v= \cfrac { s }{ t }

where:

v is the speed in m/s

s is the distance in m

t is the time in sec

Velocity, (\overset { \rightarrow }{ v } ) is the rate at which displacement changes as time changes. It can be found by dividing the displacement travelled by the time taken. The unit for velocity is also m/s or ms-1. The equation for velocity is:

\overset { \rightarrow }{ v } =\cfrac { \overset { \rightarrow }{ s } }{ t }

where:

\overset { \rightarrow }{ v } is the velocity in m/s

{ \overset { \rightarrow }{ s } is the displacement in m

t is the time in sec

Average Velocity

Often we describe the speed in a problem or scenario as the average speed. This is because for any typical journey a vehicle or object in motion will speed up and slow down.


Converting Units of Speed and Velocity

While the SI unit for speed and velocity is m/s, problems may often state units in km and hours. In these problems you may be required to convert km/hr into m/s. The simple way to make this conversion is:

  • to convert from km/hr into m/s – divide by 3.6
  • to convert from m/s into km/hr – multiply by 3.6

Example 1:

A jogger ran the following path shown in pink. Determine the distance and the displacement covered on her run from the diagram:

Answer:

Distance = 9km

Displacement = 6.7 km in the direction shown (in later sections you will be required to indicate using a bearing)


Example 2:

A pigeon flies north for 3 hours and covers 72 km. Calculate:

a) the speed of the pigeon

b) the velocity of the pigeon

Answer:

a) v= \cfrac { s }{ t }

v=\cfrac { 72 }{ 3 }

v=24 km/hr (6.7 m/s)

b) \overset { \rightarrow }{ v } =\cfrac { \overset { \rightarrow }{ s } }{ t }

Using working in part a)

\overset { \rightarrow }{ v } =24 km/hr north (6.7 m/s north)

 

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