# Speed kills / physics puzzle

Discussion in 'General Discussion' started by Softus, 18 Jan 2009.

1. ### tim west

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I was analysing blondinis answers which look linear

as stated before its not a trick question and you mention im misunderstanding the braking effect

Without any hard values to go by i'll take a wild guess and say that all the answers will be the same 11 MPH? Correct?

edit

Hang on has reaction time got something to do with it?

3. ### Softus

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If you need hard values then I'll give you hard values - what would you like?

Nope.

That's intuitively wrong as well, because you wouldn't expect a car doing 100mph/200mph/999mph to be able to reduce it's speed to 11mph in the same distance as a car that was doing merely 32mph.

4. ### tim west

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I've edited my post about reaction time, has that got anything to do with it?

5. ### 2scoops0406

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I agree nearly. 11, 18 and 23

Stopping distance at 30 MPH (13.411 m/s) = 23 metres.

therefore using v^2 = u^2 + 2as plug in the figures

v = 0
u = 13.411
s = 23

0^2 = 13.411^2 + 46a

solve for a

a = -179.9 / 46 a = -3.91 m/s^2

work out v at 32 MPH (14.31m/s) 35 MPH (15.65 m/s) and 38 MPH (16.99 m/s)

i.e @ 32 MPH

v^2 = 14.31^2 + 2 * -3.91 * 23 = 24.9 m/s
v = 4.99 m/s = 11 MPH

@ 35 MPH

v^2 = 15.65^2 + 2 * -3.91 * 23 = 65.1 m/s
v = 8.1 m/s = 18 MPH

@ 38 MPH

v^2 = 16.99^2 + 2 * -3.91 * 23 = 108.8 m/s
v = 10.4 m/s = 23 MPH

6. ### tim west

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I thought we didnt need formulas

7. ### Softus

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Notwithstanding that, the simpler form of the equation recognises that 'a' and 's' are stated to be the same, ergo:

v1^2 - u1^2 = v2^2 - u2^2

And, since u1 is stated to be zero:

u2^2 = v2^2 - v1^2

So u2 = root (v2^2 - v1^2)

i.e. u2 = root (v2^2 - 900)
__________________________

So, taking the answer for 40mph, which is that a child who would be missed by a car originally doing 30mph would be hit at 26.5mph by a car originally doing 40mph, does it strike you as being quite important to drive slowly in built-up areas?

After all, if you managed a sustained speed of 40mph through a 3-mile stretch of urban roads, you stand to gain merely 90 seconds. Is that a sufficient 'reward' for taking the risk of maiming or killing a child?

8. ### tim west

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This post was originally inserted above but made it onto another thread by mistake from a mods error, the original post is as follows:

I forgot that you mentioned that reaction times are not part of it earlier on in the thread so im baffled now, whats the answer?

9. ### Softus

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Well, the correct answers, to the nearest mph, are:

32: 11
35: 18
38: 23

The non-linear element of this is that the distance travelled while decelerating is in proportion to the difference between the squares of the starting and finishing speed, not merely the difference between the speeds.

So, in the distance needed for a car doing 30mph to come to a complete halt, the same car doing 100mph would reduce its speed to only 95.4 mph.

Reaction times, which I ignored for the purpose of this illustration, makes matters even more dangerous. If you take a reasonable average reaction time of 0.75 seconds, then the results are different. I'll work them out later and post them here.

11. ### Thermo

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now i see where you are coming from softus. When i read your first post i was about to put fingers to keyboard, but having waited i see your very valid point.

12. ### 2scoops0406

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17 MPH
22 MPH
27 MPH

Based upon relative speed plus reaction time remaining constant.

13. ### 2scoops0406

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All completely theoretical of course, depends upon the car you drive.

14. ### Softus

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To account for reaction time, we have to know something about the stopping distance, so for the sake of this I'll take the figures from Highway Code as being accurate and applicable.

When the car is doing 30mph, we are told that it travels 9m in the 'thinking time' and another 14m when braking to zero.

Deriving the reaction time and overall distance from the above, the speed at the moment of impact will be:-

32: 13
35: 21
38: 26

And, in case it's interest, the driver of a car doing 77mph would not even have started to brake by the time the child became a pizza on the windscreen.

15. ### Softus

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It's not "completely theoretical", you utter wazzak.

Why do you think the number of child pedestrians being killed by cars is on the increase?

16. ### 2scoops0406

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30 MPH = 13.411 m/s

The driver stopped exactly in front of the child. with a stopping distance (highway code of 23 m) and a reaction time of 0.75 seconds, he was 30.1 meters away when he braked.

If he was traveling at 32 MPH he was still 30.1 meters away from the child but he was traveling at 14.31 m/s therefore when he braked he was 19.37 meters away which calculates at 16 MPH

@ 35 = 22 MPH

@ 38 = 28 MPH

17. ### 2scoops0406

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Stats please, number of road deaths was at an all time min last year.

All cars are the same? moron!! A Merc S class brakes from 30 - 0 in the same time as a Rover, errr, yeah, ok.

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