Expert: Abe Mantell - 1/3/2006

Question
Working through Morris Kline's Calculus book. I enjoy mathematics but apparenly I don't have an aptitude for it. My question is from one of the problem sets. "The landing velocity of an airplane 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." His answer is 20,000 mi/hr^2. After several fruitless appraoches I have to admit I don't know how to arrive at the correct answer.

Answer
Hello Bruce!

Let the constant rate of deceleration be -a.
So, dv/dt=-a, thus v(t)=-at+vo, where vo=v(0),
which in this case is 100 mi/hr.  Hence,
v(t)=-at+100, since dx/dt=v(t)...we get
x(t)=-(1/2)at^2 + 100t +xo, where xo=x(0).

We know the plane went from 100 mi/hr to 0 mi/hr
in 1/4 mile.  Thus, 1/4=-(1/2)at^2 + 100t, with xo=0.
All we need is the time required for the plane to
come to a stop.  Letting v=0, we solve for t:
0=-at+100, so t=100/a...now substitute this into
the other equation: 1/4=-(1/2)a(100/a)^2 + 100(100/a)
and now solve for a...
1/4=-5000/a + 10000/a ==> 1/4=5000/a ==> a=20,000 mi/hr^2
or about 8.15 ft/sec^2

OK?

Abe