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Re: [Phys-L] f'(t) / g'(t) question



On 04/08/2016 06:52 AM, Lulai, Paul wrote:

if x=f(t) and y = g(t) then dx/dt = f'(t) and dy/dt = g'(t) would be
velocity vectors.
so far so good.

OK.

The question:
is g'(t) / f'(t) a velocity value? can it be used to determine
instantaneous velocity values? [1]

No. It doesn't even have dimensions of velocity.

You can think of it as the tangent of the /heading/.
Specifically, atan2(y', x') is the heading, measured CW from north:

x' y' atan2(y', x')
0 1 0
1 0 90
0 -1 180
-1 0 270

Note that the conventional atan2(y,x) asks for the y argument first.
Don't ask me why.

My knee-jerk response is that it is not a velocity value.

OK.

However, i don't
know if there is a way to use this to find the instantaneous velocity.

You can't. In polar coordinates it is the /direction/
of the velocity, without regard to the magnitude.

I am
pretty-much brain-locked into x' ^2 + y'^2 = v^2 when dealing with just
kinematics. [2]

That gives the magnitude, without regard to the direction.

Is there a useful or common thing that is appropriate here?

The two ideas [1] and [2] are complimentary: direction and magnitude.