Speed & Velocity · Revision Notes · Physics

Speed

The speed of an object is the distance it travels per unit time
Speed is a scalar quantity
- This is because it only contains a magnitude (without a direction)
For objects that are moving with a constant speed, use the equation below to calculate the speed:
$s p e e d = \frac{d i s \tan c e t r a v e l l e d}{t i m e t a k e n}$
Where:
- Speed is measured in metres per second (m/s)
- Distance travelled is measured in metres (m)
- Time taken is measured in seconds (s)

A hiker might have an average speed of 2.0 m/s, whereas a particularly excited bumble bee can have average speeds of up to 4.5 m/s

In some cases, the speed of a moving object is not constant
- For example, the object might be moving faster or slower at certain moments in time (accelerating and decelerating)
The equation for calculating the average speed of an object is:

$A v e r a g e s p e e d = \frac{d i s t a n c e t r a v e l l e d}{t i m e t a k e n}$

The formula for average speed (and the formula for speed) can be rearranged with the help of the formula triangle below:

Average speed, total distance and time taken equation triangle

Formula triangles are really useful for knowing how to rearrange physics equations
To use them:

Cover up the quantity to be calculated, this is known as the 'subject' of the equation
Look at the position of the other two quantities
- If they are on the same line, this means they are multiplied
- If one quantity is above the other, this means they are divided - make sure to keep the order of which is on the top and bottom of the fraction!

In the example below, to calculate speed, cover-up 'speed' and only distance and time are left
- This means it is equal to distance (on the top) ÷ time (on the bottom)

How to use formula triangles

The velocity of a moving object is similar to its speed, except it also describes the object’s direction
- The speed of an object only contains a magnitude - it’s a scalar quantity
Velocity is therefore a vector quantity because it describes both magnitude and direction
- e.g. ‘15 m/s south’ or ‘250 mph on a bearing of 030°’

Two objects can have the same speed but a different velocity

This means velocity can also have a negative value
- E.g. a ball thrown upwards at a velocity of 3 m/scomes down at a velocity –5 m/s, if upwards is considered positive
- However, their speeds are still 3 m/s and 5 m/s respectively
The equation for velocity is very similar to the equation for speed:

$v e l o c i t y = \frac{d i s p l a c e m e n t}{t i m e}$

$v = \frac{s}{t}$

Where:
- v = velocity in metres per second (m/s)
- s = displacement, measured in metres (m)
- t = time, measured in seconds (s)
Velocity is a vector quantity, so it uses displacement, s, rather than distance which is scalar.

Speed