Converting Position/Time to Velocity/Time Graphs

[john lavoie]

Homework Statement

What are the steps needed to convert a chart giving position and time into a velocity vs time chart and then graphing them both. How would i go from a d-t graph to a v-t graph and what steps do i take?

Homework Equations

The Attempt at a Solution

 

[debajyoti datta]

have you taken elementary course in calculus?...if not then then you can go for " calculus for dummies"

 

[RUber]

Generally, your velocity is the slope of the distance vs. time plot.
If you are moving at a constant velocity, your d-t plot will be linear.
Conversely, if you have a velocity vs. time plot, and want to see the distance, that will be the area under the curve.
As debajyoti pointed out, these are fundamental concepts in calculus. But if you consider them for distance travelled, they are also somewhat intuitive.

 

[Biker]

Well first if you have to define what motion is happening in the d-t graph.
Does it have acceleration? Does it resemble a constant speed? Or is the object moving at all?

Lets consider the third situation..
What do you think the graph will be like?
Note that d is a position. If it changes then the object is moving otherwise then it doesnt.
Now If it doesn't move, Then the velocity is = ?

How about a constant speed?
What do you think the graph will be like?
If it is constant speed then, it should move the same distance over a period of time.
Okay so how do you get the speed?
As it is constant then I just need to calculate the change of distance over time and it will give me the value.
So when I draw the v-t graph, How should I draw the v?

What about if it accelerates (Constant acceleration)?
Then the d-t should look like a curve because the change in distance changes over time.
How I am supposed to find the acceleration?
Well, you have the equations of motion. Once you get the acceleration.
You can draw the v-t.
Choose some arbitrary time and place it in the equations, get the final velocity and mark that on the graph. Connect the points and you will end up with a straight line

 

[john lavoie]

Well first if you have to define what motion is happening in the d-t graph.
Does it have acceleration? Does it resemble a constant speed? Or is the object moving at all?

Lets consider the third situation..
What do you think the graph will be like?
Note that d is a position. If it changes then the object is moving otherwise then it doesnt.
Now If it doesn't move, Then the velocity is = ?

How about a constant speed?
What do you think the graph will be like?
If it is constant speed then, it should move the same distance over a period of time.
Okay so how do you get the speed?
As it is constant then I just need to calculate the change of distance over time and it will give me the value.
So when I draw the v-t graph, How should I draw the v?

What about if it accelerates (Constant acceleration)?
Then the d-t should look like a curve because the change in distance changes over time.
How I am supposed to find the acceleration?
Well, you have the equations of motion. Once you get the acceleration.
You can draw the v-t.
Choose some arbitrary time and place it in the equations, get the final velocity and mark that on the graph. Connect the points and you will end up with a straight line

lets say I am given a d-t graph showing curves, how would i show that on a v-t graph

 

[debajyoti datta]

lets say I am given a d-t graph showing curves, how would i show that on a v-t graph

you can show v-d plot but time will not be there...in 3 dimensions however you can show all of them... :)

 

[RUber]

Here's a video that explains the idea.


If you share your curve and try to interpret it, we can provide more pointed feedback. However, in general, your question has been answered.
The slope of your position curve at any point in time will be the velocity at that time.

 

[john lavoie]

Here's a video that explains the idea.


If you share your curve and try to interpret it, we can provide more pointed feedback. However, in general, your question has been answered.
The slope of your position curve at any point in time will be the velocity at that time.

time between each of these points is 0.1 second
Position (m)(forward)
0.13

0.14

0.16

0.20

0.23

0.26

0.31

0.36

0.42

0.49

0.56

 

[RUber]

For example, in your first interval, position changes 0.01 m in 0.1 sec, which is a rate of 0.1 m/sec. So for your velocity plot, you will have a constant 0.1 m/sec over the same interval.

I would recommend you first plot this as constant velocity over each interval, and then discuss interpolation strategies later.