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## Racetrack

By David, 27 January 2016 Activity

Draw a racetrack.

See how fast you can whip around the racetrack in this maths game!

### You will need

• 5 mm square graph paper
• A friend or friends
• A different coloured pen for each person

### What to do

1. Draw a top-down view of a racetrack on the graph paper. The track should be about 5 boxes wide, and form a loop or a figure eight.
2. Draw in a start/finish line
3. You and each of your friends should each grab a different coloured pen. Use that pen to draw an ‘x’ on an intersection of grid lines on or just behind the starting line. This ‘x’ represents your race car. No two ‘x’s should be on the same intersection – that would cause a collision.

You can move one space in any direction.

4. Decide who is going first.
5. Players will take it in turns to make a move. After everyone has made a move, the circle starts again, with the first player again taking a move.
6. On the first turn, each player can draw an ‘x’ in any of the eight intersections surrounding their current ‘x’. Remember that you can’t run into anyone else’s car. Then draw a line between your starting ‘x’ and the ‘x’ you just drew, so you can work out where you’ve been, and how fast you are going.

First, continue in the same direction as last move. then make a small change.

7. On the second go, and every go afterwards, look at how far and in what direction your car moved last go. Put a dot on the intersection that is the same distance and direction from your current race car. An easy way to do this is to count how many boxes up or down you moved last time, and how many boxes left or right you moved last time, and then count out those distances to find where to put your dot. Then, put an ‘x’ on that intersection, or one of the eight intersections directly surrounding the dot.
8. If you run off the track, put your ‘x’ on the intersection nearest to where you fell off the track. Then miss a go, and finally, when you start driving again, you start with no speed built up.

If you fall off the track, start again as close to the collision point as possible.

First person across the finish line wins!

9. Once you’ve played a few races, try adding some extra rules. Maybe you want to have a rolling start (cars are already moving at the start of the race) or maybe the cars have a tank of nitrous oxide that they can use for a one off speed boost!

### What’s happening?

After playing this game a few times, you’ll notice that it’s a lot harder to slow down when you’re moving fast. Often when you’re approaching a corner, moving one box per turn slower can be the difference between a really good corner, and falling off the outer edge of the track.

Imagine a race car moving at four boxes a turn. In order to stop, it will take three turns of slowing down – first it moves three boxes, then two, and finally one box. In total, it takes six box spaces in order to stop.

Now imagine a race car moving at six boxes a turn. It will take this fast car five turns to stop, which is two turns more time than the slower car. The big difference is in the distance it takes. As the fast car slows down, it moves five boxes, then four, three, two and one box before stopping. It takes a total of 15 boxes to stop, or almost three times the distance that the slower car took!

### Real-life maths

The distance needed to stop a car is called the stopping distance, and it is very important to road safety. Although technologies such as anti-lock breaking systems (ABS) and better tyres have made cars better at braking, the main factor that determines a car’s stopping distance is its speed. A small reduction in your speed will mean a big reduction in your stopping distance because it takes less time to stop, and you’re going slower while you do it.

Stopping distance is a very important factor when working out speed limits. On an open highway, you can see a long way, and drivers have a lot of warning if something dangerous is happening up ahead. On a suburban street, it is often harder to see, and there are more pedestrians, cyclists and cars slowing down to turn or park. Near schools, speed limits are very slow because young children can be hard to see, and might not know how dangerous running on the road can be.

Cutting the speed limit from 60 to 40 kilometres an hour will cut the stopping distance from about 32 metres to 17 metres. Also, if an accident does occur in a 40 zone, it will happen at a much lower speed, causing less severe injuries.

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