# 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**

**(a) ***The final speed is 1m/s and the original or initial speed is 30m/s. So we just plug these in the derivitive equation and solve for time (t).*

* Therefore* it takes about 113 s to slow down to 1m/s. We can also check this answer by using the points (113,1).

answers are equal, so th etime it takes to slow down (113s) is correct.

**(b) ***First off we have to find the parent function. We do this by seperating the variables, antidifferentiating, and than solving for the s(t).*

This equation looks odd with the weird exponent, but i don't know what I did wrong, if I even did anything wrong. It doesn't look right.

Well now we have to solve for C. For this we need another point on the parent function like (0,0), but I can't seem to solve for another point. I'm not sure if we can use the speed formula (v=d/t), which would give us the point (113,113). However that does not seem correct.

Anyways once we find that point we than solve for the constant k by plugging in all the numbers into the parent equation. Now we can solve for s(113) since it takes 113s to slow from 30m/s to 1m/s.

**(c)** First we have to find the time it takes to slow down all the way to 0m/s from 30m/s. Then we can use that time and just plug it into the parent function, and we have our answer.

will be solved by crystal =)

## Comments (0)

You don't have permission to comment on this page.