Because the drag on objects moving through air increases as the square
of the velocity, the acceleration of a bicyclist coasting down a slight hill
is (v) = a - cv where a and c are constant. Determine the velocity of
the bicyclist as a function of distance if the velocity is zero when x=0.
Also determine the maximum velocity that the cyclist attains.
dx/dt = v
dv/dt = a-cv
The Attempt at a Solution
x = -v/c - (a/c^2)*ln(a-cv)/a
v = (a - ae^-ct)/c
t = -(cx + v)/a = -(1/c)*ln(a-cv)/a