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Speed kills / physics puzzle

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

  1. tim west

    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? ;)
     
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  3. Softus

    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

    tim west

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    I've edited my post about reaction time, has that got anything to do with it?
     
  5. 2scoops0406

    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

    tim west

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    I thought we didnt need formulas :eek:
     
  7. Softus

    Softus

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    Which part of "what's your intuitive answer" did you misunderstand? :confused:

    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

    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

    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.
     
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  11. Thermo

    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

    2scoops0406

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    17 MPH
    22 MPH
    27 MPH

    Based upon relative speed plus reaction time remaining constant.
     
  13. 2scoops0406

    2scoops0406

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

    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

    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

    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

    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.

    And you can't add up.
     
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