Is Displacement Always Positive in Two-Dimensional Space?

  • Context: High School 
  • Thread starter Thread starter lrl4565
  • Start date Start date
  • Tags Tags
    Displacement
Click For Summary

Discussion Overview

The discussion revolves around the concept of displacement in two-dimensional space, particularly whether displacement can be negative or is always positive. Participants explore definitions, relationships between displacement, distance, speed, and velocity, and the implications of these concepts in one-dimensional versus two-dimensional motion.

Discussion Character

  • Conceptual clarification
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants assert that displacement is the shortest distance between two points and can be either positive or negative, depending on the direction.
  • Others propose that in two-dimensional motion, displacement is a vector quantity with components along each axis, implying that direction is essential for understanding displacement.
  • One participant questions the relationship between displacement and magnitude, suggesting that displacement might always be positive when calculated using the Pythagorean theorem.
  • There is a discussion about the definitions of speed and velocity, with some noting that speed is related to distance and is always positive, while velocity is related to displacement and can have a direction that may be positive or negative.
  • Participants discuss examples involving circular motion, noting that while the distance traveled may be significant, the displacement can be zero, leading to different average speed and velocity values.
  • Questions arise about the definitions of acceleration, with some participants clarifying that acceleration relates to changes in velocity, not speed.

Areas of Agreement / Disagreement

Participants express differing views on whether displacement can be negative in two-dimensional space, with some asserting it can be while others focus on its vector nature. The discussion remains unresolved regarding the implications of these definitions and their applications.

Contextual Notes

Participants reference various definitions and examples, indicating that their understanding may depend on specific contexts or interpretations of displacement, distance, speed, and velocity. There is also a lack of consensus on the relationship between these concepts in two-dimensional motion.

lrl4565
Messages
19
Reaction score
0
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.
 
Physics news on Phys.org
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.
 
lrl4565 said:
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.
 
  • Like
Likes   Reactions: gracy
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?
 
Last edited:
lrl4565 said:
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.
 
My book tells me that acceleration is "how fast your speed changes". Is it speed or velocity?
 
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.
 
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.
 

Similar threads

  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 10 ·
Replies
10
Views
3K
  • · Replies 13 ·
Replies
13
Views
2K
  • · Replies 2 ·
Replies
2
Views
15K
  • · Replies 16 ·
Replies
16
Views
2K
  • · Replies 1 ·
Replies
1
Views
4K
  • · Replies 13 ·
Replies
13
Views
3K
  • · Replies 5 ·
Replies
5
Views
3K
  • · Replies 33 ·
2
Replies
33
Views
4K