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

[Patatra Chowdhury]

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.

 

[PeroK]

The question isn't "why doesn't it mean something?", but "what would it mean?"

 

[Herman Trivilino]

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.

 

[Vanadium 50]

Signifies what exactly?

 

[sophiecentaur]

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.

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.