Re: Problem

[John Mallinckrodt <ajmallinckro@CSUPOMONA.EDU>]

On Tue, 18 Sep 2001, Hugh Haskell wrote:

> In the trajectory case, there are terms involving *gt* in the
> expression for the speed, Hence the speed is *not* constant,
> even if the component subject tot he acceleration happens at
> some instant to be zero. The time derivative of the speed is
> *not* zero, hence it *is* changing.

Yes, the speed is "a function of time" and is, therefore, "not
constant", but there can still be *instants* of time *at* which
its time derivative is zero and, therefore, *at* which the speed
is "not changing."

Or simply consider the following.  Speed always has a nonnegative
value.  Therefore, if its *value* is zero at some instant of time,
then its *time derivative* at that same instant of time can *only*
be either zero or undefined.  (Draw a graph.)

For example, in the case of constant acceleration projectile
motion, the time derivative of the speed at the top of the
trajectory is zero if the velocity has a nonzero horizontal
component and is undefined otherwise.  (Somewhat more precisely it
has differing "left" and "right" limits, being -g on one side and
+g on the other.)

John Mallinckrodt      mailto:ajm@csupomona.edu
Cal Poly Pomona          http://www.csupomona.edu/~ajm