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Classical Mechanics Questions

  1. Apr 14, 2012 #1
    1. The problem statement, all variables and given/known data

    An airplane touches down at a speed of 100m/s. It travels 1000 metres along the runway
    while deceleration at a constant rate before coming to rest. How long did it take the airplane to come to rest on the runway?

    Xi=0m/s Xf=1000m Vix=100m/s

    2. Relevant equations
    Xf=Xi+Vixt

    3. The attempt at a solution
    1000=0+100t
    t=10s

    Why is the answer 20 s? and why does this formula fail?
     
    Last edited: Apr 15, 2012
  2. jcsd
  3. Apr 14, 2012 #2
    It seems that your particle isn't affected by any forces, thus it keeps on moving in the same direction with constant speed.
     
  4. Apr 14, 2012 #3
    the plane need decelation the speed from 100 m/s to 0 m/s so the mean velocity is 50 m/s then t = 20 s.
     
  5. Apr 14, 2012 #4
    Your math is correct, but your equation is wrong. I've calculated it and the answer
    t=20s is correct. Try revisiting your equations.
     
  6. Apr 15, 2012 #5
    No, it's not wrong at all. you could use the equation and mean velocity. But if you need to use the standard equation. it will be
    Xf = Vi*t + 1/2 a*t^2 (1)
    Vf = Vi + a*t (2)
    a = (Vf - Vi) /t (3)
    Xf = Vi*t + 1/2 (Vf -Vi) * t
    Xf = 1/2 (Vf +Vi)*t (4)
    Xf = 1000 m , Vi = 100 m/s , Vf = 0 m/s
     
  7. Apr 15, 2012 #6
    Isn't this just constant acceleration motion? Just use the constant acceleration formulae to find the acceleration first.

    Useful formulae:
    v2 - vi2 = 2aΔx
    v=vi + at
     
  8. Apr 17, 2012 #7
    yes, you are right.
    You can use the simple form of energy conservation
    1/2 m vf2 - 1/2 m vi2 = m a Δx
    => v2 - vi2 = 2aΔx
    Thanks.
     
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