Is Displacement Always Positive in Two-Dimensional Space?

[lrl4565]

What the book says: Displacement is the shortest distance between two points, and can be positive or negative.

Question: What about when you're working with two axes? To find the point you use the pythagorean theorem... making displacement always positive. Is this related to magnitude?Distance is...? I know that it measures every step between two points (not the shortest distance like displacement), but as for sign, I'm guessing that it is always positive because Speed = Distance/ Time and Speed is always positive.

 

[Stonebridge]

There are various definitions but one that relates to what you have said is that
"displacement is distance traveled in a particular direction".
Speed is defined in relation to distance, and velocity in relation to displacement.
This means that displacement and velocity are vectors, and thus have direction, whereas speed and distance have only magnitude.

If you walk half way around a circle you displacement would be 2r (in a particular direction) but the distance traveled would be πr.
If you walk all the way round your distance traveled would be 2πr and your displacement zero. Your average speed and velocity would also be different for this reason.

 

[jtbell]

What the book says: Displacement is the shortest distance between two points, and can be positive or negative.

This is a for a one-dimensional system, where the motion is back and forth along a line.

Question: What about when you're working with two axes?

In two or more dimensions, displacement is a vector quantity. It has components along each of the axes. (Actually, even in one dimension we can speak of displacement as being a vector that has only one component.)

If your textbook eventually talks about vectors, it will probably talk about vector displacements.

 

[lrl4565]

What I've gathered:

Speed = Distance/ Time

Velocity = Displacement/ Time

Magnitude = length
Direction = positive or negative

Alright, so if a particle travels 10 meters to make a complete circle in 5 seconds, the speed is 2 m/s, while the velocity is 0 m/s?

Is acceleration speed/ time or velocity/time?

In addition: they represent speed with the letter V? Really? What do they represent Velocity with?

 

[jtbell]

Direction = positive or negative

For one-dimensional motion, yes. For two-dimensional motion you need an angle, for example 35 degrees north of east.

Alright, so if a particle travels 10 meters to make a complete circle in 5 seconds, the speed is 2 m/s, while the velocity is 0 m/s?

I would say "average speed" and "average velocity." The instantaneous speed may vary at different points on the circle. The instantaneous velocity must vary at different points on the circle, because the direction changes from one point to the next.

 

[lrl4565]

My book tells me that acceleration is "how fast your speed changes". Is it speed or velocity?

 

[jtbell]

Velocity. If you keep your speed constant but change your direction of motion, you accelerate. An example is circular motion at constant speed (uniform circular motion). You have an acceleration whose direction is always towards the center of the circle, and some force must produce that acceleration via F = ma.

 

[lrl4565]

Velocity uses displacement/ time, Speed uses distance/ time, but when measuring instantaneous speed or velocity, they're basically equal aside from the fact that velocity has a direction.