Find deceleration from distance and initial velocity

  1. I have just started a calculus book, and I cant figure out how to solve this problem:

    1. The problem statement, all variables and given/known data
    The landing velocity of an airplane (i.e., the velocity at which it touches the ground) is 100 mi/hr. It decelerates at a constant rate and comes to a stop after traveling 1/4 mile along a straight landing strip. Find the deceleration or negative acceleration.

    2. Relevant equations

    3. The attempt at a solution
    a = x
    v = xt + C
    v = xt + 100
    s = (x/2)t^2 + 100t + C
    1/4 = (x/2)t^2 +100t

    I'm not sure what to do next.
  2. jcsd
  3. rock.freak667

    rock.freak667 6,231
    Homework Helper

    solve for t using the quadratic equation formula.
  4. HallsofIvy

    HallsofIvy 41,267
    Staff Emeritus
    Science Advisor

    In addition to 1/4= (x/2)t^2+ 100t, which says that the airplane moved 1/4 mile in t hours, you have xt+ 100= 0 since the airplane came to a stop (has speed 0) in that time.
    From xt= -100, x= -100/t.

    Replace x in 1/4= (x/2)t^2+ 100t with that and solve the resulting linear equation for t. Once, you have t, you can solve for x from x= -100/t.
  5. Thanks Ivy, don't know why I didn't think of that.
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