# Challenging! Find maximum deceleration and speed (not max)

1. Dec 18, 2013

### mia2

1. The problem statement, all variables and given/known data
Given $$\frac{d^2s}{dt^2}=-Ae^{s/B}\biggl(\frac{ds}{dt}\biggr)^2$$ Show that maximum deceleration (where $A,B$ are constants, $v=v_0$, and $s=-\infty$) is $\frac{v_0^2}{2eB}$.

Use the substitution $v=\frac{ds}{dt}$.

2. Relevant equations
See above.

3. The attempt at a solution
Using the substitution, I get $\frac{d^2s}{dt^2}=-Ae^{s/B}(v)^2$. Furthermore, using $v=v_0$ and $s=-\infty$ and using the original function, I get $v=e^{-ABe^{s/B}}v_0$. Combining these two equations, I get
$$\frac{d^2s}{dt^2}=-Ae^{(s/B)-(2ABe^{s/B})}v_0^2$$.
With $s=-\infty$, I end up with:
$$\frac{-Av_0^2}{e^{2AB}}$$, which isn't what's given in the problem. Not sure what I'm doing wrong.

Last edited: Dec 18, 2013
2. Dec 18, 2013

### SteamKing

Staff Emeritus
Your Latex came out garbled. Try hitting the Preview button before you post to make sure everything formats properly.

3. Dec 18, 2013

### mia2

Ok, I've fixed it now. Do you have any suggestions for my physics problem?

4. Dec 19, 2013

### Saitama

Why do you think acceleration is maximum at $s=-\infty$? I don't see how you can find a maximum only by inspection. You will have to differentiate the acceleration function and set the derivative to zero.