Seth wrote:
| If the object is to change its velocity it must have a non-zero value for
| acceleration; i.e. to change one's velocity requires an acceleration
(either
| by changing one's speed or direction).
Consider the displacement y(t):
(Think of it as a vertically tossed ball on a very strange planet!)
y(t) =200t/3 - 5t^2 + (t^3)/6 - (t^4)/480
Take three derivatives and plot y(t) , v(t) , a(t) and j(t) from t=0 to 40.
Observe that the thing seems to "hang" momentarily at y=333.33:
At t=20 the object has reached the top of its path. It then turns around and
falls.
But at t=20, the velocity, the acceleration and the jerk are ALL zero!
It only keeps going (turns around) because the derivative of its jerk is
non-zero (-1/20). ALL other derivatives of y(t) are zero at t = 20.
This should disabuse one of (sometimes spoken, sometimes implied) arguments
that the acceleration (and/or jerk) cannot be zero at a turnaround point
simply because the velocity is obviously changing.
You can concoct for yourself more bizarre (but possible) motions in which
the velocity keeps changing even though (at some time) it and all of its
derivatives but the Nth one are zero, N being as large as you please.