Physics

Fox

### Summary

- The
**speed**of an object is a measure*how fast it moves*. Speed is defined by: \[ \text{speed} = \frac{ \text{distance} }{ \text{time} } \] - This equation can be put into a
**formula triangle**:

Use your finger to cover up the one you want to find, and the remaining two will show you how to find it. - The
**SI unit**of speed is**metres per second**(m/s): - Other units for speed include
**miles per hour**(mph) and**kilometres per second**(km/s).

They ask me where the hell I'm going

At a thousand feet per second

Speed is something you've already come across is everyday life; if you're in a car you might be moving at a speed of 60 miles per hour (mph).

Today we're going to define what speed is, and show how to do calculations with it.

The **speed** of an object is a measure of *how fast it moves*.

Okay, so what's the difference between a fast thing and a slow thing?

A fast thing **moves a longer distance** than a slow thing does **in the same amount of time**.

e.g. In \(10\) seconds, a quick fox might travel \(100\text{m}\), but a lazy dog might only travel \(20\text{m}\).

We define speed to be the **distance travelled divided by the time taken**:

So the fast fox has speed, \( \text{s} = \frac{\text{d} }{\text{t} } = \frac{100 \text{m} }{10 \text{s} } = 10 \text{ m/s} \)

and the lazy dog has speed, \( \text{s} = \frac{\text{d} }{\text{t} } = \frac{20 \text{m} }{10 \text{s} } = 2 \text{ m/s} \)

Note how the unit of speed (\( \text{ m/s} \) ) magically appeared when we *calculated* the speed!

As we have just found, the SI unit of speed is **m/s**:

m/s isn't the *only* unit of speed, it's just the *scientific* unit. On this page we've already mentioned two other units of speed: ‘feet per second’ and ‘miles per hour’. What all of these units have in common is that they all have the form: [distance unit] / [time unit]. They *need* to have this form because speed = distance / time !

**NB:** m/s is always spoken aloud as “metres **per** second”, like how mph is spoken as “miles **per** hour”. Any unit with a divide sign in the middle is spoken as “per”.

\( \text{speed} = \frac{ \text{distance} }{ \text{time} } \) can be written as a **formula triangle**:

Many people find these useful. Here's how they work:

Use your finger to cover up the symbol *you want to find*, and the remaining two symbols will show you *how to find it*:

For example, if you want to find the speed, cover up \( s \) with your finger. We can see that \( d \) is on top of \( t \). Therefore, \( \text{s} = \frac{ \text{d} }{ \text{t} } \)!

Similarly, if we want to find the distance, cover up \( d \) with your finger. We can see that \( s \) is next to \( t \). Therefore, \( \text{d} = \text{s} \times \text{t} \) !

Let's solve some example questions using this method...

**NB:**A formula triangle can be used

*any time*you have an equation which looks like A = BC or A = B/C. (You can do this because the triangle doesn't ‘know’ what the symbols inside it actually

*mean*).

**Usain Bolt runs 24m in 2s. What is his speed?**

We can sum up this question as:

speed = **?**

distance = 24m

time = 2s

Using the definition of speed, we know that **speed = distance / time**. Alternatively, we could cover up \( s \) on the formula triangle with our finger to reveal: \( \text{s} = \frac{ \text{d} }{ \text{t} } \).

Therefore, Usain Bolt's \( \text{speed} = \frac{24 \text{m} }{2 \text{s} } = 12 \text{ m/s} \).

That's absolutely *R a p i d*.

**A drone travels at 15 m/s for 4 seconds. How far does it travel?**

We can simplify this question as:

speed = 15m/s

distance = **?**

time = 4s

We need a formula to get distance from speed and time. Covering up \( d \) on the formula triangle shows \( s \) and \( t \) next to each other. Therefore, \( \text{d} = \text{s} \times \text{t} \).

Therefore, the drone travels a distance \( \text{d} = 15 \text{m/s} \times 4\text{s} = 60 \text{m} \).

**A tsunami wave travels at 200m/s. It is 10km away from the shore. How long until the tsunami reaches the shore?**

We can more succinctly write this question as:

speed = 200m/s

distance = 10km = 10,000m

time = **?**

We need a formula to get distance from speed and time. Covering up \( t \) on the formula triangle shows \( d \) on top of \( s \). Therefore, \( \text{t} = \frac{ \text{d} }{ \text{s} } \).

Therefore, the time taken \( = \frac{ 10,000 \text{m} }{ 200 \text{m/s} } = 50 \text{s} \).

When we are just using SI units (m, s, m/s), things are relatively straightforward. Unfortunately in the real world, people will use all sorts of units that *aren't SI units*.

Consider the following question:

**A Formula One racing car can travel 30 km in 5 minutes. What is its speed in m/s?**

First, we approach this as we have done for the previous 3 examples:

1) Find the relevant formula: (speed = distance/time)

2) Find the relevant quantities in the formula: (distance = 30 km, time = 5 minutes).

3) Put these quantities into the formula: (speed = 30 km/5 mins = **6 km/minute**).

However, we have come across a problem. Our speed is in units of km/minute, but the question wants this the answer in **m/s** !

To fix this issue, we need to add another step between 2) and 3): **in order to get the speed in m/s, we need to get the distance in m, and the time in s**.

For distance, this isn't so bad. 1km = 1000m, so 30km = 30,000m.

For time, we need to use that 1 minute = 60s. Therefore, 5 minutes = 5 × 60s = 300s. (Feel free to use a calculator for this.)

So our quantities (step 2) are now: distance = 30,000m, time = 300s.

Finally, we put this into our formula (speed = distance/time), to get speed = 30,000m / 300s = **100m/s**.

The formula triangle is really a trick for doing something called *rearranging formulae*.

For example, when finding the distance an object moves, what we're really doing is multiplying \( \text{speed} = \frac{ \text{distance} }{ \text{time} } \) by time on both sides of the equation:

\( \text{s} = \frac{ \text{d} }{ \text{t} } \)

\( \text{s} \times \text{t} = \frac{ \text{d} }{ \text{t} } \times \text{t} \)

\( \text{s} \times \text{t} = \text{d} \times \frac{ \text{t} }{ \text{t} } \)

\( \text{s} \times \text{t} = \text{d} \)

\( \text{distance} = \text{speed} \times \text{time} \)

(Because \( \frac{ \text{t} }{ \text{t}} = 1 \).)

You'll use this technique in future when studying **algebra** in maths class.

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