Chapter 9, Problem 36P

An airplane uses a parachute and other means of braking as it slows down on the runway after landing. Its acceleration is given by $a=-0.0035v^2-3$ m/s³. Since $a=\frac{dv}{dt}$ , the rate of change of the velocity is given by:

$a=\frac{dv}{dt}=-0.0035v^2-3$

Consider an airplane with a velocity of 300 km/h that opens its parachute and starts decelerating at t = 0 s.

(a) By solving the differential equation, determine and plot the velocity as a function of time from t = 0 s until the airplane stops.

(b) Use numerical integration to determine the distance x the airplane travels as a function of time. Make a plot of x versus time.