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

• I
• Patatra Chowdhury
In summary, the conversation discusses the difference between the significance of a graph of velocity versus time compared to a graph of displacement versus time squared. It is noted that while the slope of the velocity versus time graph has dimensions of acceleration and equals the acceleration, the slope of the displacement versus time squared graph also has dimensions of acceleration but does not equal the acceleration. The question of the significance of this difference is raised, but it is ultimately concluded that this discussion may not lead to any concrete conclusions.
Patatra Chowdhury
TL;DR Summary
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?

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.

## 1. Why is the v vs. t graph significant?

The v vs. t graph is significant because it represents the relationship between an object's velocity and time. It allows us to visualize how an object's velocity changes over time and can provide valuable information about its motion.

## 2. What does the slope of a v vs. t graph represent?

The slope of a v vs. t graph represents the object's acceleration. A steeper slope indicates a greater acceleration, while a flatter slope indicates a smaller acceleration.

## 3. Why doesn't the s vs. t^2 graph signify?

The s vs. t^2 graph does not signify because it does not represent a physical relationship. It is simply the result of taking the square of the time values, and does not have any physical meaning or significance.

## 4. Can a v vs. t graph be used to determine an object's position?

No, a v vs. t graph cannot be used to determine an object's position. It only shows the relationship between velocity and time, and does not provide any information about the object's position.

## 5. How is a v vs. t graph different from an s vs. t graph?

A v vs. t graph represents the relationship between velocity and time, while an s vs. t graph represents the relationship between position and time. The v vs. t graph shows how an object's velocity changes over time, while the s vs. t graph shows how its position changes over time.

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