"Acceleration Vector" question

[markraz]

Hi, I have a couple questions regarding Acceleration Vectors. An Acceleration Vector is supposedly the first derivative of a position vector (is that right??)
This picture says that the Acceleration Vector is the normal at a given point??


So my question is, if i zoomed in really really close on a curve (green) and selected 2 points close together and drew a line segment between the points (red)


then I draw a line perpendicular to the red line (the blue line). Would the blue line be in the same direction as the Acceleration Vector??


thanks in advance

 

[Romsek]

velocity is the first derivative of the position vector
acceleration is the 2nd derivative of the position vector

 

[Dr.Peterson]

An Acceleration Vector is supposedly the first derivative of a position vector (is that right??)

First derivative of velocity, second derivative of position.

This picture says that the Acceleration Vector is the normal a a given point??

If the speed (magnitude of velocity) is constant. Presumably your source is talking only about that case.

In general, acceleration has both tangential and normal components.

Would the blue line be in the same direction as the Acceleration Vector??

Approximately, if speed is constant.

As an example, in circular motion at a constant speed, acceleration is toward the center. In orbital motion in an ellipse, acceleration is toward the focus (sun), which is not always perpendicular to orbital motion, and the planet's speed is varying.

 

[markraz]

Thanks, ok so if I zoomed in really close to the curve (green) and picked twp points. then drew a line through those 2 points (red), then I drew another line perpendicular to the red line (blue line), would that go in the direction of the acceleration vector?

thanks

 

[Romsek]

As Dr. Peterson said this would be the case if the speed is constant.

If there is tangential acceleration going on as well then the acceleration and velocity vectors aren't necessarily normal to one another.

 

[markraz]

As Dr. Peterson said this would be the case if the speed is constant.

If there is tangential acceleration going on as well then the acceleration and velocity vectors aren't necessarily normal to one another.

oh ok thanks

 

[markraz]

ok thanks

what does "speed" is that a derivative too?
I assume these terms relate to physics. What term do they use in regular math for 'speed'?

thanks

 

[Romsek]

speed is the magnitude of the velocity vector

 

[topsquark]

I assume these terms relate to physics. What term do they use in regular math for 'speed'?

You will occasionally find that Introductory level Mathematics (College Algebra or higher) might use the term "rate" for speed. As acceleration is the "rate" of change of velocity this is rather ambiguous. Generally the higher you go in Mathematics the less often you see the term rate being used.

-Dan

 

[markraz]

thanks !!! everyone