# Math Help - an AP Calculus AB review question

1. ## 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.

v[final]=1;v[original]=30;m=50;k=1.5;t=113.383

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.

2. Originally Posted by Jziffra
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.

v[final]=1;v[original]=30;m=50;k=1.5;t=113.383

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.
$\Delta x = \int_{t_1}^{t_2} v(t) \, dt
$

3. Thank you.

I've run into a problem with the third part in that I'm getting an illogical answer for my time:

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

it's given that ds/dt = v[final] = v[original]e^-(k/m)t; I know that m = 50, k = 1.5, v[original] = 30 and I'm trying to find t when v[final] = 0, but that gives me ln(0/30)/(-1.5/50) which is impossible with the natural log of 0.

Does anybody know where I went wrong here?

4. Originally Posted by Jziffra
Thank you.

I've run into a problem with the third part in that I'm getting an illogical answer for my time:

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

it's given that ds/dt = v[final] = v[original]e^-(k/m)t; I know that m = 50, k = 1.5, v[original] = 30 and I'm trying to find t when v[final] = 0, but that gives me ln(0/30)/(-1.5/50) which is impossible with the natural log of 0.

Does anybody know where I went wrong here?
$v(t) \to 0$ as $t \to \infty$

$
\Delta x = \lim_{b \to \infty} \int_0^b v(t) \, dt
$