Writing Velocity as dx/dt in K= ∫mvdv = ∫m dx/dt dv - Does it Make Sense?

  • Context: Undergrad 
  • Thread starter Thread starter STAR GIRL
  • Start date Start date
Click For Summary

Discussion Overview

The discussion revolves around the expression of velocity in the context of kinetic energy, specifically examining the equation K= ∫mvdv = ∫m dx/dt dv. Participants question the validity of representing velocity (v) as the derivative of position with respect to time (dx/dt) and seek clarification on this relationship.

Discussion Character

  • Conceptual clarification, Technical explanation

Main Points Raised

  • Some participants question how velocity can be expressed as dx/dt in the context of the kinetic energy equation.
  • Others assert that velocity is defined as the rate of change of position with respect to time, thus supporting the expression v=dx/dt.
  • A participant seeks further clarification on the definition of velocity and its relationship to the equation.

Areas of Agreement / Disagreement

There is a general agreement on the definition of velocity as dx/dt, but some participants express uncertainty about its application in the kinetic energy equation.

Contextual Notes

The discussion does not resolve the implications of using v=dx/dt within the context of the kinetic energy equation, leaving open questions about its application.

STAR GIRL
Messages
24
Reaction score
0
In equation K= ∫mvdv = ∫m dx/dt dv, how can we write v at any time t as dx/dt?? Does it make any sense??
 
Physics news on Phys.org
STAR GIRL said:
In equation K= ∫mvdv = ∫m dx/dt dv, how can we write v at any time t as dx/dt?? Does it make any sense??
This is how velocity is defined. How do you define velocity?
 
  • Like
Likes   Reactions: Orodruin
fresh_42 said:
This is how velocity is defined. How do you define velocity?
I just want to know that how can we write v as dx/dt
 
Well, velocity is the rate of change of position (x) with respect to time (t). So v=dx/dt by definition.
 
  • Like
Likes   Reactions: STAR GIRL
Ibix said:
Well, velocity is the rate of change of position (x) with respect to time (t). So v=dx/dt by definition.
Yup I got it. Thanks
 

Similar threads

Undergrad Power done by work on a continuous body isn't the derivative of work?
  • · Replies 11 ·
Replies
11
Views
2K
Graduate Inconsistency between definitions of power and work in continuum mechanics?
  • · Replies 9 ·
Replies
9
Views
1K
Undergrad Non-Newtonian description of an accelerated object
  • · Replies 8 ·
Replies
8
Views
2K
Graduate Treating Velocity as Independent of position till the end in Lagrangian Mechanics
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad Doubt about variable mass systems
  • · Replies 30 ·
2
Replies
30
Views
3K
Undergrad Newton's Second Law - variable mass case
  • · Replies 14 ·
Replies
14
Views
3K
Undergrad How Does the Chain Rule Apply to Newton's Second Law in Calculus?
  • · Replies 10 ·
Replies
10
Views
3K
Undergrad The effect of a field on a particle depends on the particle velocity?
  • · Replies 5 ·
Replies
5
Views
1K
Undergrad How can engineers get away with splitting differentials in dynamics?
  • · Replies 3 ·
Replies
3
Views
3K
Undergrad Filling a rigid tire from a pressure regulated compressed air line
  • · Replies 67 ·
3
Replies
67
Views
6K