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Mathematics To Slow You Down

Blog Date - 25 January 2018

Despite the mathematics in the video it does not make sense...until...until I really put my mind to it.

Imagine a car can lose 10mph every second. At 70 mph it takes 7 seconds to stop. At 100mph in 7 seconds it will be doing 30mph - surely? Yes, yes it would. But the car doing 100mph does not HAVE 7 seconds to stop. He has a certain DISTANCE, not TIME to stop within. He is going faster so he will arive at the fallen tree sooner. 

Let me draw you a chart.

Speed Distance Travelled in 1 second Distance Travelled Overall
70 to 60 29 metres 29 metres
60 to 50 24.5 metres 53.5 metres
50 to 40  20 metres 73.5 metres
40 to 30 15.5 metres 89 metres
30 to 20 11 metres 100 metres
20 to 10  6.5 metres 106.5 metres
10 to 0 2 metres 108.5 metres

So in our particular scenario it takes 108.5 metres for our car to stop from 70mph in 7 seconds. The car doing 100mph does NOT have 7 seconds to stop - he has 108.5 metres to stop. Let me draw another chart.

Speed Distance Travelled in 1 second Distance Travelled Overall
100 to 90 42.5 metres 42.5 metres
90 to 80 38 metres 80.5 metres
80 to 70 33.5 metres 114 metres

As you can see the car doing 100mph travels 114 metres in 3 seconds and is still doing OVER 70mph by the time he reaches the 108.5 metre mark. 

Is this still counter intuitive? Well what if both cars had much better brakes and could brake a lot sharper? Let us repeat the tables but this time both cars can slow down by 20mph every second.

Speed Distance Travelled in 1 second Distance Travelled Overall
70 to 50 27 metres 27 metres
50 to 30 19 metres 46 metres
30 to 10  10 metres 56 metres
10 to 0 1 metre 57 metres

This time the car doing 70mph can stop in 3.5 seconds and a distance of 57 metres. Let us look at the car travelling at 100mph.

Speed Distance Travelled in 1 second Distance Travelled Overall
100 to 80 40 metres 40 metres
80 to 70 17 metres 57 metres

Once again taking into account a bit of rounded numbers the car doing 100mph at the start of the experiment is still doing 70mph by the time it passes the car that stopped from 70mph.

A small image of the formula used on this page
You can use this formula if you wish. 

Physics is a cruel master. My CBF125 puts out about 11bhp and can reach maybe 70mph on a good day with the wind behind me. Therefore Latchy's 121bhp Street Triple should be capable of at least 700mph because it is over 10 times more powerful! Nope, physics doesn't work that way.

The next time you're about to overtake that pain-in-the-ass dawdling car or truck be sure the road ahead is safe and clear, otherwise a bunch of nerds with calculators and pencils might just bite you in the buttocks really hard.

Or as Scotty said "Ya canny change the laws of Physics, Jim"

A big powerful Nissin brake on a modern motorcycle
Modern brakes are excellent but they're still subject to science.

Do you have a motoring safety article you'd like to publish on Bikes And Travels? Contact

Reader's Comments

Ian Soady said :-
I hope those people that witter on about speed not contributing to crashes read and more importantly understand this.

What a lot of people don't grasp is just how short a distance is required to stop from 30 mph - as you suggest in your tables, a couple of car's lengths. Yet people persist in crashing into stuff when they could perfectly well stop.

25/1//2018 3:57:09 PM UTC
Ren - The Ed said :-
I'm not scared of heights Ian, I am scared of floors. Heights never killed anyone it's the floor they landed on that did. We should ban floors!!! The same applies with speed. Don't lower speed limits - ban obstacles like houses, corners, street lights, barriers, walls, curbs, roundabouts, hills, other road users...

I suppose the safest place to go fast must be empty space.
25/1//2018 4:25:26 PM UTC
Bob said :-
The older I get the more space I leave between me and the vehicle in front. I've had enough get-offs to be able to instantly recall that sickening lurch in the stomach as you pass the point of no return and I don't want to experience it again. Interestingly enough though I do enjoy that feeling of calm acceptance that comes over you as you fly through the air / skate along the tarmac....

When I did my part one test back in the 80's the instructor there asked us learners "what do brakes do?" and keen to impress I think I called out "slow the bike down", he countered with "No! Brakes slow the rotation of your wheels" - that's the best piece of advice I've ever received and I carry it in my mind every time I'm operating a motor vehicle.
Also I do agree with the opinion that off-road riding makes you a better on-road rider, off-road you can experience the limits of grip and traction in a lower speed and (relatively) safe environment, therefore when back on the road you can feel when the front is on the edge of it's grip or when the back is about to slip.

26/1//2018 9:40:14 AM UTC

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