Why v vs. t graph signifies but s vs. t^2 doesn't ?

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Discussion Overview

The discussion revolves around the significance of different types of graphs in physics, specifically comparing the velocity versus time graph (v vs. t) and the displacement versus time squared graph (s vs. t²). Participants explore the implications of these graphs in terms of their dimensions and what they represent in the context of motion and acceleration.

Discussion Character

  • Exploratory
  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • Some participants question the significance of the s vs. t² graph compared to the v vs. t graph, suggesting that the latter has a clearer meaning in the context of physics.
  • One participant notes that while both graphs have slopes with dimensions of acceleration, only the slope of the v vs. t graph directly represents acceleration.
  • Another participant raises the question of what significance the graphs hold, implying that the transition between physics and mathematics may not always yield meaningful insights.
  • There is a suggestion that the s vs. t² graph could represent distance traveled under constant acceleration, which some may find significant, though this is debated.

Areas of Agreement / Disagreement

Participants express differing views on the significance of the graphs, with some arguing that the v vs. t graph is more meaningful while others challenge the relevance of the s vs. t² graph. The discussion remains unresolved regarding the implications of these graphs.

Contextual Notes

Participants have not reached a consensus on the significance of the graphs, and there are unresolved questions about the interpretations of the slopes and areas under the curves.

Patatra Chowdhury
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TL;DR
This is a question which crossed my mind when I was analyzing the dimensions of the quantities.
Why v vs. t graph signifies but s vs. t^2 doesn't ? This is a question which crossed my mind when I was analyzing the dimensions of the quantities.
 
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The question isn't "why doesn't it mean something?", but "what would it mean?"
 
Are you asking why a graph of ##v## versus ##t## has some significance but a graph of ##s## versus ##t^2## doesn't have any significance? Certainly the area under each graph has different dimensions, but the slope of each graph has dimensions of acceleration. But it's only the slope of the ##v## versus ##t## graph that equals the acceleration. The slope of the ##s## versus ##t^2## graph has dimensions of acceleration but it's not equal to the acceleration.
 
Signifies what exactly?
 
Vanadium 50 said:
Signifies what exactly?
I think it just goes to demonstrate that hopping in and out between Physics to Maths may be no more than a 'brain exercise' and may or may not have 'significance'.
I have noticed that the question of what Maths Is All About has come up quite frequently, or at least been inferred, in a number of recent threads.
Mister T said:
Are you asking why a graph of v versus t has some significance but a graph of s versus t2 doesn't have any significance?
Isn't that just the distance traveled under constant acceleration? I would call that very significant.
But this sort of discussion will never get us anywhere, imo.
 

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