# 2.04 Speed (i)

Speed is a measure of how fast an object is moving
It is defined as the rate of change of distance over time
( ie how the distance travelled by the object changes with time)

s = Δd/Δt

• s = speed - in metres per second (ms-1)
• Δd = change in distance - in metres (m)
• Δt = corresponding change in time - in seconds (s)

Example
An object travels a distance of 25 m and the time taken to travel this distance is 5 seconds. What is the object's speed?
s = Δd/Δt
s = 25/5
s = 5ms-1

[Note: due to the limited numbers of letters available to represent physical quantities the same symbol "s" has been used for both speed and displacement!
We need to be careful with the correct interpretation of the symbols used in equations and sometimes alternative symbols are used to avoid confusion.
e.g. It should be clear from the context of any questions what s represents but in the event of any confusion, say in an example that involves both displacement and speed, it is best to choose an alternative symbol for one of the quantities e.g. x, is also commonly used in place of s for displacement ( it can also be used for distance too!).
]

## Average speed

The speed of an object may not be constant, in this case using the equation will give the object's average speed (we can write (save) if we wish to to emphasise this). This is a common situation when travelling by car. The speed of the car will vary over the journey and it may even be stationary for some periods. However by the dividing the total distance travelled by the time taken we can calculate the average speed of the car over the journey.

## Instantaneous speed

Instantaneous speed is a more difficult concept because it "literally" means speed at a single instant in time! However at a single instant in time an object would appear to be frozen as if recorded in a photograph! So when we are referring to instantaneous speed we mean the object"s speed over an very small period of time.

To clarify the difference between average and instantaneous speed consider the following:
A car travels a total distance of 10.8km in 30mins, but when it is 10 mins into the journey it is travelling 25m every second
Average speed = 10.8x103metres/1800 seconds = 6 metres per second
Instantaneous speed at 10 mins = 25metres/1 second = 25 metres per second

In this example we are taking the instantaneous speed to be over a period of one second compared to the average speed taken over half an hour.

(note if we were considering a much faster moving particle such as an electron we might consider the speed over a period of 1 second as its average speed and consider its instantaneous speed to be over a much smaller period such as a micro-second (a millionth of a second!))