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Math Help - Acceleration

  1. #1
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    Exclamation Acceleration

    A plane lands on a runway at 100m/s. It then brakes with a constant deceleration until it stops 2 km down the runway. Acceleration = -k, for some positive constant k. By integrating with respect to x, find k, and find v^2 as a function of x.

    Could someone please help?
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  2. #2
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    Quote Originally Posted by Sunyata View Post
    A plane lands on a runway at 100m/s. It then brakes with a constant deceleration until it stops 2 km down the runway. Acceleration = -k, for some positive constant k. By integrating with respect to x, find k, and find v^2 as a function of x.

    Could someone please help?
     <br />
\frac{dv}{dt} = -k<br />

     <br />
v = \frac{dx}{dt}<br />

     <br />
\frac{dv}{dt} \cdot \frac{dt}{dx} = -\frac{k}{v}<br />

    \frac{dv}{dx} = -\frac{k}{v}

     <br />
v \, dv = -k \, dx<br />

    \frac{v^2}{2} = -kx + C

     <br />
v^2 = -k_2 x + C_2<br />

    at x = 0 , v = 100 m/s

     <br />
100^2 = C_2<br />

    v^2 = -k_2 x + 100^2

    at x = 2000 m , v = 0

    0 = -k_2(2000) + 100^2

     <br />
k_2 = 5<br />

     <br />
v^2 = -5x + 100^2<br />
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