Example of x0 in the kinematic equation for displacement

Click For Summary

Discussion Overview

The discussion revolves around the kinematic equation for displacement, specifically focusing on the initial position variable, x0, and its possible values in different scenarios of motion. Participants explore examples involving both vertical and horizontal motion, examining how the choice of origin affects the value of x0.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant asks for an example where x0 is not zero in the kinematic equation x = x0 + v0 * t + .5 * a * t^2.
  • Another participant explains that x0 represents the initial position and can be any value, providing an example of dropping an object from a height of 5 meters, where x0 = 5 m and v0 = 0 m/s.
  • A participant requests an example where both x and x0 are not zero.
  • One participant clarifies that x(t) changes over time and will be non-zero until the particle hits the ground in the vertical example provided.
  • A request is made for a horizontal motion example where both x and x0 are not zero.
  • Another participant suggests starting a particle 5 meters from the origin with an initial velocity of 5 m/s in the horizontal direction.
  • One participant reflects on the confusion regarding whether x0 should be zero, indicating it depends on the context of the problem.
  • A later reply emphasizes that the choice of origin determines the value of x0, illustrating this with the previous example of dropping an object from a height.

Areas of Agreement / Disagreement

Participants generally agree that the value of x0 can vary based on the chosen origin of the coordinate system. However, there is some confusion regarding when to set x0 to zero, indicating that the discussion remains somewhat unresolved.

Contextual Notes

Participants note that the choice of origin can significantly affect the values of x0 and x, and that different scenarios may lead to different interpretations of these variables.

e-zero
Messages
58
Reaction score
0
In the kinematic equation x = x0 + v0 * t + .5 * a * t^2, can someone give me an example in which x0 has a value that is not zero?
 
Physics news on Phys.org
Hi e-zero! ##x_{0}## is just the initial position of the test particle that you are looking at the trajectory of under constant acceleration; similarly ##v_{0}## is just the initial velocity of the trajectory. You can choose them to be whatever you want them to be. I can for example drop my object from a height of 5 meters from the ground, starting at rest, in which case ##x_{0} = 5 \text{m}## , ##v_{0} = 0 \text{m /s}## , and (ignoring air resistance) the equations of motion become ##x(t) = 5 \text{m} - \frac{1}{2}gt^{2}##. Hope that helps friend!
 
Ok, is there an example where both x and x0 are both not zero?
 
##x(t)## is a function of time so it will change its value at every instant of time. In the example I gave above, ##x(t)## is the height of the particle from the ground so it will be non-zero up until the first time the particle hits the ground.
 
Can you give an example that does not involve vertical, but horizontal motion in which x and x0 are both not zero?
 
Sure! Choose an origin and take a particle located 5 meters horizontally from that origin and give it an initial kick of 5 meters per second in the horizontal direction.
 
Ok. I was just confusing myself. It all depends on the question if you should take x0 to be zero or not.
 
Indeed! Good luck with your studies friend :)
 
Thanks
 
  • #10
e-zero said:
Ok. I was just confusing myself. It all depends on the question if you should take x0 to be zero or not.

Not really. It depends on where you want the origin of your system of coordinates to be. In WBN's example, he chose the ground as origin. That's why x_0 in his case was 5m. For the same example he could have chosen its origin 5 meters above the ground, in which case x_0 would have been 0.
 
  • #11
Ok, I see.
 

Similar threads

High School Kinematic equations ##\textbf{purely}## from graphs
  • · Replies 49 ·
2
Replies
49
Views
4K
Undergrad How can angular displacement be larger than 2pi?
  • · Replies 20 ·
Replies
20
Views
3K
Graduate Influence of initial shift on undamped frictionless forced oscillations
  • · Replies 10 ·
Replies
10
Views
1K
High School Misleading Textbook Equation for vf^2=vi^2 + 2ad
  • · Replies 3 ·
Replies
3
Views
3K
High School Rotational Kinematics -- questions about a=mg sin(theta) / (m+I/R^2)
  • · Replies 6 ·
Replies
6
Views
3K
Undergrad Kinematics cases with non-constant acceleration
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Understanding the 1-D Kinematics Equations
  • · Replies 8 ·
Replies
8
Views
3K
Undergrad I'm calculating more energy out than I put in
  • · Replies 138 ·
5
Replies
138
Views
9K
High School Kinematic Equations: View List & Explanations
  • · Replies 2 ·
Replies
2
Views
3K
Undergrad Seemingly Simple Kinematics Question
  • · Replies 7 ·
Replies
7
Views
2K