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mia2
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Homework Statement
Given $$\frac{d^2s}{dt^2}=-Ae^{s/B}\biggl(\frac{ds}{dt}\biggr)^2$$ Show that maximum deceleration (where [itex] A,B [/itex] are constants, [itex]v=v_0[/itex], and [itex]s=-\infty[/itex]) is [itex]\frac{v_0^2}{2eB}[/itex].
Use the substitution [itex]v=\frac{ds}{dt}[/itex].
Homework Equations
See above.
The Attempt at a Solution
Using the substitution, I get [itex]\frac{d^2s}{dt^2}=-Ae^{s/B}(v)^2[/itex]. Furthermore, using [itex]v=v_0[/itex] and [itex]s=-\infty[/itex] and using the original function, I get [itex]v=e^{-ABe^{s/B}}v_0[/itex]. Combining these two equations, I get
$$\frac{d^2s}{dt^2}=-Ae^{(s/B)-(2ABe^{s/B})}v_0^2$$.
With [itex]s=-\infty[/itex], 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.
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