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# Speed and Velocity

### Speed and Velocity

Speed is a measurement that describes how fast an object is travelling.

**Units** for speed

Speed is...

We can measure speed using different units. Which are the three units in the picture?

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**Miles**, **kilometres** and **metres** are all measures of ______________.

**Hours** and **seconds** are both measures of ______________.

All units for speed include a measure of _____________ and a measure of ___________.

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What is the SI unit for speed?

**Measuring** Speed

It's sports day and your friend is about to start a race. They've asked you to find out how fast they cycle. What two quantities do you need to measure?

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To measure these quantities, you'll need...

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The race begins and you start your stopwatch. The track is $400 \space m$ long and your friend crosses the finish line in $50s$. Now you have to calculate their speed; how many metres did they cycle *per* second?

You worked out you speed like this $\frac{400 \space m}{50 \space s}=8 \space m/s$. What is the correct **formula** for speed then?

So the formula for speed is $speed = \frac{distance}{time}$

This gives you units that include both measures of distance and measures of time, like $m/s$, $km/h$ or $mph$

Here we can see a graph with the measurements from the race.

At time $50s$ your friend reached the distance of $400m$.

At what point did your friend start the race?

Your friend finished the race at $(50, 400)$ and you calculated the speed at which they cycled to be $8\:m/s$. Can you guess what part of the graph might represent the speed?

In any graph, the slope of the line is calculated by $\frac{change\:in\:y}{change\:in\:x}$.

For a distance-time graph, this is the same as $\frac{change\:in\:distance}{change\:in\:time}$ which is just the speed!

Vectors and Scalars

When we talk about speed, we are giving magnitude to how fast an object is travelling. What type of quantity is this?

When we talk about speed in a given direction, we call it **velocity**. This is...

We talk about velocity when we care about what direction a moving object is travelling in.

Speed simply gives us the magnitude of the velocity.

Summary!

The speed of an object is how fast an object is going

By that we mean how far that object has gone in a given time, for example $10 \space m$ in $5 \space s$

You calculate speed like this $speed = \frac{distance}{time}$

For example $\frac{10 \space m}{5 \space s}=2 \space m/s$

That means that units for speed have a measure of distance and a measure of time

For example $m/s$, $km/h$ or $mph$

Speed is a scalar quantity.

Velocity is a **vector** quantity.