### GCSE Physics

Energy
Forces
Forces and Motion
Waves in Matter
Electricity
Magnetism and Electromagnetism
Particle Model of Matter
Atomic Structure
Space Physics

# Distance, Displacement, Speed and Velocity

Quantities can be categorised as either scalar or vector. Scalar quantities only have a magnitude, whereas vector quantities have both a magnitude and a direction.

• Distance is a scalar quantity because it only takes into account the magnitude and not the direction. For example, 15 metres.
• Displacement is a vector quantity as it takes into account both magnitude and direction. For example, 80 metres north.

## Speed

Speed is considered a scalar quantity, as it only takes into account the magnitude and not the direction. For example, if someone is running at a speed of 5 miles per hour (mph), we know how fast they are travelling but we don’t know the direction.

The table below shows the speeds that people and objects can be travelling at.

It is also important to know the speed of sound in air, which is roughly 343 metres per second (m/s). However, sound waves travel at different speeds through different mediums.

To calculate the average speed of an object, you need to know the distance that the object travelled and the time it took for that distance to be travelled. With the equation:

• S = Speed in metres per second (m/s)
• D = Distance in metres (m)
• T = Time in seconds (s)

These triangles above are used to help us remember the formula. Sometimes, we might need to solve for distance or time instead of speed. Therefore, we need to know how to rearrange the formula to work out the various subjects.

### Example

Calculate the speed of a jogger who covered a distance of 60 m in 20 s.

60m ÷ 20 s = 3 m/s

The speed = 3 m/s

The unit for speed is metres per second (m/s).

## Velocity

Velocity is a vector quantity because it takes into account magnitude and direction. For example, if a car is driving at 50 miles per hour (mph) west. It takes into account how fast the car is going (50 mph) and the direction (west).

To calculate velocity, we replace the scalar quantity of distance travelled with the vector quantity of displacement. This allows us to get the value of velocity, with the equation:

Do not confuse the S in both equations.

• In the speed equation, S mean speed
• In the velocity equation, S means displacement

Let’s use the example we used for speed, but this time calculate the velocity.

### Example

Work out the speed of a jogger who ran 60 m east in 20 s.

60m ÷ 20 s = 3 m/s east

So the answer is still m/s but as we are measuring the velocity, the direction must be taken into account. Therefore the velocity = 3 m/s east.

Quizzes