Speed with constant acceleration

Click For Summary

Discussion Overview

The discussion revolves around the interpretation of the equation v^2 = v0^2 + 2a(x - x0) in the context of speed and velocity under constant acceleration. Participants explore the relationship between speed, velocity, and the mathematical formulation of motion in physics.

Discussion Character

  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant expresses confusion about why speed is represented as v^2 in the equation, questioning the distinction between speed and velocity.
  • Another participant clarifies that v^2 refers to the speed squared, emphasizing that the equation pertains to uniformly accelerated straight-line motion.
  • A participant suggests that it would be clearer if the equation were presented as v = sqrt(v0^2 + 2a(x - x0)), indicating that the current representation may be misleading for some readers.
  • Another reply encourages viewing the equation as a relationship among variables rather than solely a formula for speed, noting the aesthetic preference for v^2 over the square root form.

Areas of Agreement / Disagreement

Participants exhibit some agreement on the interpretation of the equation in terms of motion, but there is disagreement regarding the clarity of representing speed as v^2, with some feeling it could be misleading.

Contextual Notes

The discussion highlights potential confusion stemming from the mathematical representation of speed and velocity, as well as the assumptions about the audience's familiarity with these concepts.

ahuebel
Messages
11
Reaction score
0
Using a Newton equation for position and substituting (v-v0)/a for t you can get the following formula:
v^2= v0^2+2a(x-x0) where v^2 is supposedly speed. I understood speed to be tha magnitude of velocity which is the sqrt of the sum of the squares of the components (i.e. sqrt(vx^2+vy^2+vz^2)). I seem to be missing something... how is speed then v^2? I am sure it is right in front of my face but I am just not seeing it.

TIA
 
Physics news on Phys.org
v^2 is the speed squared; v is the speed.

Realize that your formula ,v^2= v0^2+2a(x-x0), is for uniformly accelerated straight-line motion.
 
Thank you. It just seems odd that if they would state that an equation is speed as a fucnction of position it would be much better to have that equation be v = sqrt(v0^2+2a(x-x0)). It can throw simple people like me off :).
 
Think of that equation as a relationship among all the different variables, not just as a formula for finding speed. Depending upon what information is given, you may wish to use it to solve for any of the variables. (And having a single v^2 is much nicer looking than that ugly square root! :smile: )
 

Similar threads

High School Why is speed constant when centripetal acceleration is constant?
  • · Replies 24 ·
Replies
24
Views
4K
Undergrad Acceleration as a Function of Time Using Constant Power
  • · Replies 27 ·
Replies
27
Views
4K
High School Understanding F=ma: Constant Speed & Acceleration
  • · Replies 9 ·
Replies
9
Views
2K
Undergrad Speed of objects as they hit the ground
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Kinematics cases with non-constant acceleration
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Non-Constant Angular Acceleration
  • · Replies 6 ·
Replies
6
Views
3K
Undergrad How can I calculate the time for non-uniform acceleration in a circular path?
  • · Replies 13 ·
Replies
13
Views
3K
In a constant acceleration motion, Is it possible to have constant speed?
  • · Replies 11 ·
Replies
11
Views
2K
Graduate Unit Normal Vector in Acceleration
  • · Replies 17 ·
Replies
17
Views
4K
Kinematics: Acceleration of a figure skater changing direction
  • · Replies 16 ·
Replies
16
Views
2K