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

[Optikspik]

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.

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?

 

[PWiz]

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.

 

[BvU]

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...

 

[BvU]

, 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...

 

[PWiz]

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".

 

[Optikspik]

? 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?

 

[PWiz]

? 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?

 

[BvU]

? 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 ?
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Homework Equations

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The Attempt at a Solution

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Lower two pictures in post #1

main barrier: continuity or not ? for x? for v ? for a ?​

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

and then we'll take it from there.

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