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 = -0.0035v2 -3 m/s2. Since a = dv/dt, the rate of change of the velocity is given by:
dv2/dt = -0.0035v2 -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.