Ave. versus Instantaneous

1. Mar 8, 2004

gmommy

This is in my book.
Speed and velocity are defined by the following equations ..

Limit statements:
The magnitude of an object's velocity approaches its speed as the time interval approaches zero:.
Thus, the instantaneous speed of an object is the magnitude of its instantaneous velocity: v = |v|.

This is my question/s
What is the magnitude? I don't know what the mag. is OR the difference between Ave. speed and instantaneous speed
OR between Ave. and Instantaneous Velocity.
I know this probably seems like a moron question to you guys but I have just started physics. I cant find a way to 'GET' these equations.

2. Mar 8, 2004

KingNothing

Don't be worried about asking a "moronic question". We're here to help for the most part.

Average speed is basically the speed you would need to go at constantly to get from point A to point B. It's like If I was to travel by car to detroit. My average speed would be somethingn like 30 miles per hour, even though at times I was going 60 and at times I was stopped.

Instantaneous speed is the speed at any given instant. Think of it like this:

If you are accelerating at 1 meter/s^2, which is the same as saying "1 meter per second" "per second". Each second the speed increases by 1 meter per second. At time=1 second, the speed is 1 m/s. At 2 second, it's 2 m/s. At 3, it's 3. But see, the speed changes each second, that's why those are called instantaneous. At any other time, the speed may be different.

In the detroit example, being stopped might be an instantaneous speed, because I didn't get to detroit with the car stopped. But I was stopped for at least an instant.

Does that help?

3. Mar 9, 2004

HallsofIvy

Since Decker has already handled "instantaneous" versus "average", I'll look at "speed" versus "velocity".

To a physicist, "velocity" is a vector. It's not enough to say "45 miles per hour" (that's a "speed"). A velocity would have to be "45 miles per hour North, NorthEast". That is both a "magnitude" (how big it is) and a direction. The magnitude of a vector is simply its "length". I put "length" in quotes because, of course, if we are talking about velocity, it is not really "length". But that's a good way of thinking about it.

If an object is moving, in some laboratory experiment, with a speed of 10 m/s, at an angle of 45 degrees to a give "x-axis", then I can represent its velocity either by saying "10 m/s at 45 degrees to the x-axis" or by giving its "components": I think of the velocity vector as an "arrow" with length 10 (m/s though that really doesn't make sense for a "length"!) at an angle of 45 degrees to the x-axis. Drawing in the lines parallel to the x and y axes, I get a right triangle. Since sin(45)= cos(45)= &radic;(2)/2 (That's why I chose 45 degrees!), the two legs of the triangle have length 10(&radic;(2)/2)= 5&radic;(2). Those are the "x" and "y" components of the velocity. We might write that as <5&radic;(2),5&radic;(2)>
The speed is the "length" or magnitude of that vector. If we had been given the velocity as <5&radic;(2),5&radic;(2)>, we could calculate the speed by again visualizing that right triangle and using the Pythagorean theorem: the magnitude of the velocity vector (speed) is the length of the hypotenuse: &radic;((5&radic;(2))2,(5&radic;(2))2)= &radic;(50+ 50)= &radic;(100)= 10.

4. Mar 11, 2004

gmommy

DECKER & HALLS OF IVY

Thank You. I understand much more than I did PRE- Physics Forums.
Thank You for helping all of us out here. gmommy.