On 12/21/2022 7:51 PM, Richard Hertz wrote:
> 1-vector, 2-vector, n-vector....... fuck it.
One dimensional case is strictly along a single axis. Speeds,
accelerations can be positive or negative.
Two dimensional or more: You have to deal with vectors pointing in
directions other than strictly forward and backward. Orbits, curves and
so forth.
>
> Given a(t) for an object moving along x-axis, then
What is a? Acceleration? Position?
>
> IF da/dt = 0, the acceleration peaked or is constant.
If so, a(t) is acceleration, da/dt=0 is a zero "jerk", the third
derivative of displacement.
>
> IF da/dt > 0, the acceleration is increasing, so the object is gaining velocity (speed). It's ACCELERATING.
If the acceleration (one dimensional physics definition) is already or
has become positive, and the speed is also positive. Your "ACCELERATING"
is the common usage of the word in this case.
>
> IF da/dt < 0, the acceleration is decreasing, so the object is losing velocity (speed).
No, it loses velocity only if the acceleration is negative. The
acceleration could switch from positive to negative if da/dt < 0, or it
could still be positive after factoring in da/dt < 0 (for positive
speed). Think of a car accelerating hard from a start (you floor it)
but shortly you let off on the gas just a little, so it's still going
faster and faster, just not as much.
> It's DECELERATING, like in
> the re-entry of a spacecraft.
That's the common usage of the word, where the speed's absolute value
decreases. Usually thought of as a positive speed and a negative value
of acceleration.
What of a car going in reverse and then the brakes are applied? Is the
car accelerating, decelerating or something else?
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