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Car drive S units in T time ,prove that there is a point where acceleration > 4S/T^2

  1. Dec 22, 2009 #1
    1. The problem statement, all variables and given/known data
    Car start to drive from point A to point B in a straight line ,
    The distance from A to B is S, the time the car drove is T
    Prove that there is a point in the drive where the acceleration of the car does not lower in absolute value from [tex]\frac{4S}{T^{2}}[/tex]

    the car start the drive from speed 0 and end the drive in speed 0
    I know this is physic related question but I have in in calculus 2

    2. Relevant equations
    I almost sure you have to solve the question with taylor polynomial


    3. The attempt at a solution
    When I try built taylor polynomial when f(x) is the speed around x0 = when the speed reach S/T that is the average speed , the speed must reach the average speed

    f(X) = f(x0) + f'(c)(x-x0)
    f(x) = S/T +f'(c)(x-x0)

    Now I do this for x=0 and for x=T and I can get that if the x0 in [0,T/4] or in [3T/4,T] f'(c) that is the acceleration is above [tex]\frac{4S}{T^{2}}[/tex]

    When I try to build the polynomial when f(x) is the location and again around x0 = the time the car speed reach S/T, It does not seem to add up, Because I don't really know what value to give to f(x0)...
    Thank you for the help.
     
  2. jcsd
  3. Dec 22, 2009 #2
    Re: car drive S units in T time ,prove that there is a point where acceleration > 4S/

    Well... Vadim is your teacher?

    Do it this way:
    x(t)= x(0)+v(0)*t + a(c1)*t^2/2 when 0<c1<t...
    So we'll get: x(t)=a(c1)/2 * t^2
    If t=T/2 -> x(T/2) =a(c1)*T^2 /8....

    Around T we'll get:
    x(t) = S + a(c2)/2 * (t-T)^2 .... Put T/2 as t... Put both things you've got in equality and you're done :)
     
  4. Dec 22, 2009 #3
    Re: car drive S units in T time ,prove that there is a point where acceleration > 4S/

    Isn't the internet small
    Thank you very much..
    This was my very first try, But I thought , Ha c1 isn't c2 each one has a diffrent area and I got confused and stooped going this way.
    ...
    Thanks.
     
  5. Dec 22, 2009 #4
    Re: car drive S units in T time ,prove that there is a point where acceleration > 4S/

    The whole world is a small place to live in :)

    Anyway, which other courses you took this semester?
     
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