Originally Posted by

**yoman360** A body is coasting to a stop and the only force acting on it is a resistance proportional to its speed, according to the equation:

$\displaystyle \frac{ds}{dt}=v_f=v_0e^{(\frac{-kt}{m})}$ ; s(0)=0, where $\displaystyle v_0$ is the body's initial velocity (in m/s), $\displaystyle v_f$ is its final velocity, m is its mass, k is a constant, and t is time.

(a) If a body with mass m = 50 kg and k = 1.5 kg/sec initially has a velocity of 30 m/s, how long, to the nearest second, will it take to slow to 1 m/s?

(b) How far, to the nearest 10 meters, will the body coast during the time takes to slow from 30 m/s to 1 m/s?

(c) If the body coasts from 30 m/s to a stop, how far will it coast?