Find deceleration from distance and initial velocity

[physicsnnewbie]

I have just started a calculus book, and I can't figure out how to solve this problem:

Homework Statement

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.

Homework Equations

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]

I have just started a calculus book, and I can't figure out how to solve this problem:

Homework Statement

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.

Homework Equations

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.

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.