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Math Help - Antiderivative deceleration problem.

  1. #1
    Newbie
    Joined
    Jul 2011
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    Antiderivative deceleration problem.

    PLEASE NO PHYSICS FORMULAS: I AM TRYING TO SOLVE THIS USING THE INTEGRAL AND THE MVT. THANKS.

    A car is traveling at 100 km/h when the driver sees an accident 80 m ahead and slams on the breaks. What constant deceleration is required to stop the car in time to avoid a pileup?

    What I think I know:

    I am looking for : a(t)=(v2-v1)/t

    Where: v1=initial velocity=100 km/h
    v2=terminal velocity=0 km/h
    t=time= unknown.

    But first I need to find where s(t)=80m in order to find the time.

    This is where I seem to be stuck...do I take the first Integral of a(t) or the second and use it as s(t)? Or is there something else I'm missing?

    Thank you in advance!
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  2. #2
    Senior Member
    Joined
    Mar 2010
    Posts
    280

    Re: Antiderivative deceleration problem.

    We have

    \frac{dv}{dt}=A=const


    dv(t)=A\;dt

    Integrating we get

    \int_0^t{dv(t)}=\int_0^t{A \; dt}

    v(t)-v(0)=At

    v(t)=v(0)+At

    Now you may go on:


    \frac{dS}{dt}=v(t)
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