# Question 9

## You MAY use a calculator to solve this problem.

A body is coasting to a stop and the only force acting on it is a resistence proportional to its speed, according to the equation ; s(0) = 0, where v_{0} is the body's initial velocity (in m/s), v_{ƒ} 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 10 nearest meters, will the body coast during the time it 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?

**Solution**

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