Find deceleration from distance and initial velocity

physicsnnewbie

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.

rock.freak667

solve for t using the quadratic equation formula.

HallsofIvy

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.

physicsnnewbie

Thanks Ivy, don't know why I didn't think of that.