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Math Help - Calculating the braking distance with equations

  1. #1
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    Calculating the braking distance with equations

    Hi,
    Can anybody help me with the following as I am totally stuck! A truck is moving at 88 km h-1 and breaks to 52km h -1. What is the distance over which the breaks are used if the deceleration was 2.82 m s -2.

    I have to use one or more of the following equations - and correct SI units. I have been told to think about the energies involved. Any help will be gratefully received.

    Ek = 1/2mv^2

    W = Fd

    P = E/t
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  2. #2
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    Quote Originally Posted by jamesgill View Post
    Hi,
    Can anybody help me with the following as I am totally stuck! A truck is moving at 88 km h-1 and breaks to 52km h -1. What is the distance over which the breaks are used if the deceleration was 2.82 m s -2.

    I have to use one or more of the following equations - and correct SI units. I have been told to think about the energies involved. Any help will be gratefully received.

    Ek = 1/2mv^2

    W = Fd

    P = E/t
    I would have thought of using a motion equation but the Energy equation you have here works nicely. At 88 km/hr, the truck has kinetic energy of (1/2)m(88)^2 Joules. We don't know the trucks mass but wait on that.

    At 52 km/h, its kinetic energy is (1/2)m(52)^2 Joules. The work done by the brakes is the difference between those two: (1/2)m(52)^2- (1/2)m(88)^2= (1/2)m(52^2- 88^2) Joules.
    (Notice the order of those speeds. The truck slows down so the work done is negative.)

    The truck decelerates at 2.82 m/s^2 so its acceleration is -2.82 m/s^2. Force equals mass times acceleration (that formula isn't given here but I am sure you know it): F= ma= -m(2.82 m/s^2).

    Now use W= Fd: (1/2)m(52^2- 88^2)= -m(2.82 m/s^2)d.

    The unknown mass, m, cancels and you can solve for d.
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  3. #3
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    Thank you

    Thank you so much for not just the answer but also the clear explanation. I should be able to tackle similar equations myself now.
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