Speed and velocity Revision Notes for AQA GCSE Physics

Speed and velocity

What is speed and velocity?

Speed and velocity both tell us how fast something is moving. But they are not the same thing.

Speed is how far an object travels in a certain amount of time. It's measured in metres per second (m/s), kilometres per hour (km/h), or miles per hour (mph). Speed doesn't tell us which direction something is moving - it's called a scalar quantity.

Velocity is speed with a direction. It tells us how fast something is moving AND which way it's going. Velocity is called a vector quantity because it includes direction.

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Understanding the Difference:

A car travelling at 25 m/s has a speed of 25 m/s. But if it's travelling 25 m/s towards the north, its velocity is 25 m/s north. The direction makes all the difference!

Key differences between speed and velocity

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Critical Distinctions:

Speed = distance ÷ time (no direction needed)
Velocity = speed + direction
Speed is a scalar (just a number)
Velocity is a vector (number + direction)

Typical everyday speeds

Here are some common speeds you might encounter in daily life:

Walking: 1.5 m/s
Running: 3 m/s
Cycling: 6 m/s
Cars on UK roads: 2 to 31 m/s
Trains: up to 83 m/s in the UK
Sound waves in air: 330 m/s
Light waves: $3 \times 10^8$ m/s (very fast!)

These reference speeds help put motion into perspective and provide useful comparisons for calculations.

Calculating distance

When an object moves at a steady speed, you can work out how far it travels using this fundamental formula:

$\text{distance travelled} = \text{speed} \times \text{time}$

You can rearrange this formula in three ways:

Distance = $\text{speed} \times \text{time}$
Time = $\frac{\text{distance}}{\text{speed}}$
Speed = $\frac{\text{distance}}{\text{time}}$

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Formula Rearrangement Tip:

Remember the triangle method: cover what you want to find, and the remaining parts show you the calculation. This works for any version of the distance-speed-time relationship.

Average speed

Sometimes the speed of an object changes during its journey. When this happens, we use average speed to describe the overall motion.

$\text{Average speed} = \frac{\text{total distance travelled}}{\text{total time taken}}$

This gives us the overall speed for the whole journey, even if the object went faster or slower at different times. Average speed is particularly useful for analysing real-world motion where constant speed is rare.

When velocity changes but speed stays the same

An object can have a constant speed but a changing velocity. This happens when the object keeps moving at the same speed but changes direction.

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Real-World Example:

A car driving around a roundabout at 10 m/s. The speed stays at 10 m/s, but the velocity keeps changing because the direction keeps changing continuously as the car follows the curved path.

Working with speed calculations

Let's work through some practical examples to see how these concepts apply:

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Worked Example 1: Calculating Speed and Velocity

A cyclist travels 1800 m east in 5 minutes.

Step 1: Convert time to seconds Time = 5 minutes = $5 \times 60 = 300$ s

Step 2: Calculate speed Speed = $\frac{\text{distance}}{\text{time}} = \frac{1800 \text{ m}}{300 \text{ s}} = 6 \text{ m/s}$

Step 3: Include direction for velocity Velocity = 6 m/s east

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Worked Example 2: Calculating Distance

A person runs at an average speed of 4 m/s for 20 minutes.

Step 1: Convert time to seconds Time = 20 minutes = $20 \times 60 = 1200$ s

Step 2: Calculate distance Distance = $\text{speed} \times \text{time} = 4 \text{ m/s} \times 1200 \text{ s} = 4800 \text{ m}$

Step 3: Convert to kilometres Distance = $4800 \text{ m} = 4.8 \text{ km}$

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Key Points to Remember:

Speed is how fast something moves (no direction needed)
Velocity is speed with a direction
Use the formula: $\text{distance} = \text{speed} \times \text{time}$ (and learn to rearrange it)
Average speed = $\frac{\text{total distance}}{\text{total time}}$
An object can have constant speed but changing velocity if it changes direction

Speed and velocity (AQA GCSE Physics): Revision Notes