What is the relationship between x-t and v-t graph?

  • Thread starter Optikspik
  • Start date
  • Tags
    Drawing
In summary, the conversation revolves around drawing a v-t and a-t graph from a given x-t graph. The position-time graph appears to be a piecewise function and there are questions about the continuity of the graphs and the use of "jump" lines. It is mentioned that if the x-t graph is continuous, then by default, the graphs of its derivatives should also be continuous. However, there is a debate about whether this is always the case. The conversation ends with a request for clarification on the relationship between x(t) and v(t).
  • #1
Optikspik
23
0
I'm suppose to draw a v-t and a-t graph from a given x-t graph.

Here is the x-t graph and my attemps on the other two graphs from the x-t one.

1yMmwKP.png

WyrQK4w.png

DjswDiG.png


Howeverr

1. My teacher said that these graphs are discontinuous? Because I often see in littetaure that they drag "a vertical line" whenever something takes a jump, but it is discontinuous in the v-t graph right?

2. If it is discontinuous, and no vertical line down, If i was given the v-t graph and wanted to do a x-t rgaph. Then I would "imagine" a vertical line right? To calculate an area ?

3. Are these 2 graphs correct or what could be improved/ Whats wrong?
 
Physics news on Phys.org
  • #2
Tbh it's rather poorly drawn, so my answer may be off.
The position time graph appears to be a piecewise function. However, if it is mentioned in the question that it is continuous, then by default the graphs of all its derivatives (velocity-time and acceleration-time) should be continuous, so you must draw those "jump" lines.
If the last section of the x-t graph is parabolic, then the other graphs are correct.
 
  • #3
Pretty crude pictures. If I look at the lower two, I wonder how v can change from something to zero with a staying at zero...
 
  • #4
PWiz said:
, if it is mentioned in the question that it is continuous, then by default the graphs of all its derivatives (velocity-time and acceleration-time) should be continuous
I'd like to contradict this. A continuous function doesn't have to be continuously differentiable...
 
  • #5
BvU said:
I'd like to contradict this. A continuous function doesn't have to be continuously differentiable...
That is true in general, but I have yet to see a position time graph that has an undefined gradient.
EDIT: Unless you include some of those "jumps".
 
  • #6
? I don't understand what any of u talking is about. will their be a vertical line down on v-t graph or is there "space" between?

this is not a queestion from a book, and u understand when i draw, Its just the "principle" not exact. Do i think right?
 
  • #7
Optikspik said:
? I don't understand what any of u talking is about. will their be a vertical line down on v-t graph or is there "space" between?
Simply put - did the question say anything at all about the continuity of the x-t graph?
 
  • #8
Optikspik said:
? I don't understand what any of u talking is about. will their be a vertical line down on v-t graph or is there "space" between?

this is not a queestion from a book, and u understand when i draw, Its just the "principle" not exact. Do i think right?
Ok, fair enough. let's restart:

Homework Statement



from a given x-t graph, draw a v-t and a-t graph (top pic in post #1)
given x(t) graph does not look like top pic ? could you post it, or describe the relevant details a little better ?
​

Homework Equations



?​

The Attempt at a Solution


[/B]
Lower two pictures in post #1
main barrier: continuity or not ? for x? for v ? for a ?​
- - - - - - - - - - - - - - - - - - - - -- - - - - - - - - - -

What is, according to what you have learned, the relationship between x(t) and v(t) ?

and then we'll take it from there.

--
 

FAQ: What is the relationship between x-t and v-t graph?

What is the purpose of drawing a v-t and a-t graph from an x-t graph?

The purpose of drawing a v-t (velocity-time) and a-t (acceleration-time) graph from an x-t (position-time) graph is to visually represent the motion of an object and analyze its velocity and acceleration at different points in time. This can help in understanding the overall motion of the object and identifying any changes in its velocity or acceleration.

How do you plot a v-t and a-t graph from an x-t graph?

To plot a v-t and a-t graph from an x-t graph, you need to first determine the velocity and acceleration values at different points in time. The velocity can be calculated by finding the slope of the line on the x-t graph, while the acceleration can be calculated using the slope of the velocity-time graph. Once you have these values, you can plot them on the respective graphs.

What do the slopes of the v-t and a-t graph represent?

The slope of a v-t graph represents the acceleration of the object at a particular point in time. A positive slope indicates a positive acceleration (increasing velocity), while a negative slope indicates a negative acceleration (decreasing velocity). Similarly, the slope of an a-t graph represents the change in acceleration over time.

How can you determine the acceleration from a v-t graph?

The acceleration can be determined from a v-t graph by finding the slope of the line on the graph. The slope represents the change in velocity over time, and the acceleration is equal to the change in velocity divided by the change in time.

What can you learn from analyzing a v-t and a-t graph?

Analyzing a v-t and a-t graph can provide information about the motion of an object, including its velocity and acceleration at different points in time. By examining the slopes of the graphs, you can identify any changes in the object's velocity or acceleration, such as when it speeds up, slows down, or maintains a constant velocity. This information can help in understanding the overall motion of the object and can also be used to make predictions about its future motion.

Similar threads

Analyse motion of an oscillator: x(t)=0.2cos(12*pi*t)
Replies
5
Views
1K
Analyzing Motion: Deriving Displacement Graphs from First Principles
Replies
6
Views
1K
Constant Acceleration -- Equation for Vavge
Replies
5
Views
1K
Two launches ferrying between two landing stations along a river
Replies
23
Views
861
What is the intersection point of two objects on a position vs time graph?
Replies
10
Views
1K
Two networks described by v-i graph: Find voltages when interconnected
Replies
1
Views
830
How to Sketch a v-t Graph from a p-t Graph Using Tangents?
Replies
5
Views
4K
Graphs of y(x,t)=A Sin(kx - wt + φ) are shown below
Replies
26
Views
7K
How do I plot ψ(x,t) as a function of x at time t=a/v?
Replies
1
Views
2K
Finding g from a Compound Pendulum Graph
Replies
3
Views
7K

Hot Threads

Recent Insights

Back
Top