Re: Could you survive the ride?

[brian whatcott <inet@intellisys.net>]

At 22:28 10/23/98 -0700, Paul Goodman wrote:
> ...
> Consider the functions f(t) = t^(7/3) and g(t) = t^(5/3). Let each function
> represent the position at time t of a cart moving along a straight track.
> Both these functions vanish at the origin, have first derivatives which
> vanish at the origin, but have second derivatives which behave much
> differently at the origin -- f" vanishes, while g" goes belly up.
> ...
> There is also something that bothers me about the f-cart. Even though f" is
> zero at t = 0, f''' becomes infinite there. So the force on the f-cart is
> zero at t = 0, but it is changing infinitely fast. What would that feel
> like?
>
> Paul Goodman

There is a sublime joke here, on those folk with the mindset that reality
somehow follows from mathematical models. It is a sadness, I'm sure, but we
can't expect a useful model to track reality throughout the envelope a priori:
it's just a model!
   But I was reminded of the situation posted last year? by our absent friend
from British Columbia; the scenario where a car is driven up a slope and
then allowed to coast. It slows, then reverses, so at some point it is
stationary, but steadily decelerating... It did not take us long to agree
that yes, you could feel the difference between a stationary car (v=0,a=0)
and a decelerating one at v=0.
Try hitting the brakes when stationary!


brian whatcott <inet@intellisys.net>
Altus OK