an AP Calculus AB review question
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 ds/dt = v[final] = v[original] e^-(k/m)t; s(0) = 0, where v[original] is the body's initial velocity (in m/s), v[final] is its final velocity, m is its mass, k is constant, and t is time.
b) How far, to the nearest 10 meters, will the body coast during the time it takes to slow from 30m/s to 1m/s?
I found the first part which gave me my time, but I don't know how to continue from here. If anyone has any advice to offer, I'd greatly appreciate it. Thanks.