When we integrate function of acceleration, what do we get?

Click For Summary

Discussion Overview

The discussion revolves around the integration of acceleration functions and what the resulting functions represent, specifically in terms of velocity and changes in velocity. It touches on both indefinite and definite integrals and their implications in physics.

Discussion Character

  • Technical explanation, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant questions whether integrating acceleration yields a function for velocity or just the total change in velocity.
  • Another participant clarifies that the indefinite integral of acceleration results in the velocity function plus a constant of integration, while the definite integral represents the change in velocity between two points in time.
  • A subsequent post combines these ideas, suggesting that integrating from a fixed time to a variable time gives the change in velocity since the fixed time.
  • Another participant raises a concern about whether the integration indicates direction of change, implying that the discussion may not address vector quantities adequately.
  • A warning is issued regarding the distinction between vector quantities and their magnitudes, suggesting that the previous statements may not hold for magnitudes alone.
  • A later reply expresses confusion about the warning, indicating a lack of understanding of the distinction made.

Areas of Agreement / Disagreement

Participants express differing views on the implications of integration regarding direction and the distinction between vector quantities and their magnitudes. The discussion remains unresolved regarding these nuances.

Contextual Notes

Limitations include the potential misunderstanding of vector versus scalar quantities and the implications of integrating functions in different contexts. The discussion does not fully resolve these complexities.

AakashPandita
Messages
157
Reaction score
0
Do we get function for velocity or do we get the function for the total change in velocity?
 
Physics news on Phys.org
What kind of integral do you mean? The "indefinite integral" is a function, the "definite integral" is a number. The "indefinite integral" of the acceleration function, \int a(t)dt is the velocity function, v(t), plus a "constant of integration". The definite integral, \int_{t_0}^{t_1} a(t)dt= v(t_1)- v(t_0), change in speed between times t_0 and t_1.

We can combine the two: writing \int_{t_0}^T a(t)dt where t_0 is a fixed time and T is a variable. It gives, for any T, the change in velocity since time t_0.
 
Last edited by a moderator:
  • Like
Likes   Reactions: 1 person
okay. thanks again!
 
you said it tells us the change in speed.
that means we do not get direction of change?
 
Warning: All you wrote is correct for the vector quantities \vec{v} and \vec{a} but in general not for the magnitudes!
 
?i don't understand.
 

Similar threads

High School Explain Integration to me, please
  • · Replies 5 ·
Replies
5
Views
3K
Undergrad Ambiguity of the term "indefinite integral"
  • · Replies 11 ·
Replies
11
Views
2K
Undergrad Creating a function with specific shape, intercepts, integral....
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad What is the indefinite integral of Bessel function of 1 order (first k
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Equivalence of alternative definitions of conservative vector fields and line integrals in different metric spaces
  • · Replies 3 ·
Replies
3
Views
3K
Undergrad Should the function f to be continuous for applying MVTI or not?
  • · Replies 4 ·
Replies
4
Views
2K
High School Modelling object w/ functions, how to find volume loss from indents?
  • · Replies 9 ·
Replies
9
Views
2K
High School How do physicists know if limits exist, things are integrable, etc?
  • · Replies 12 ·
Replies
12
Views
3K
High School Functions which relate to calculus: Questions about Notation
  • · Replies 36 ·
2
Replies
36
Views
6K
High School Why don't we account for the constant in integration by parts?
  • · Replies 16 ·
Replies
16
Views
4K