How Do Displacement-Time, Velocity-Time, and Acceleration-Time Graphs Relate?

[Sean1218]

Hi, sorry for not using the template, but my question doesn't really fit.

Basically, I'm trying to move between displacement-time graphs, velocity-time graphs, and acceleration-time graphs.

Ex: http://img832.imageshack.us/img832/3391/10113039.jpg

I have a sheet filled out, but it only has some of the different types of accelerated motion (like those in the example), and I'm trying to understand why it moves like it does, rather than just the answer (I wouldn't be able to do it with any examples that aren't on my sheet if I don't know how it works).

I've been thinking trying to do this for over an hour, but the differences between how slow to fast and fast to slow curves affect the vt/at graphs is so huge, and I can't figure out how exactly it changes it (only the middle one in the screenshot is slow to fast). I've tried other resources (such as google) as well.

I know that you want people to show an effort, but this isn't really something you can show your work for, and I feel I've done all that I can do; either you know it or you don't, so I was hoping someone could explain (for other examples besides the image as well i.e. fast to slow curves, slow to fast curves, with both positive and negative slope, and both above and below the x-axis).

PS. I have a test tomorrow. I'd ask my teacher, but I've been sick the last week and he isn't giving me any time to ask questions so I'm on my own..

Thanks!

 

[dreit]

Consider the derivatives of the functions on your graphs, that may help

 

[fss]

For the first one,

-Notice that as t increases, the slope of d decreases. Since velocity is the slope of the position graph, what does a zero slope on a distance graph mean in terms of the velocity? Once you have the velocity graph, what would the derivative of the velocity (acceleration) look like?

 

[dreit]

Well if there was a slope of zero on the position graph, you would not be moving

 

[rwisz]

Hi there,

I understand your frustration and I'm happy to help explain the differences between displacement-time, velocity-time, and acceleration-time graphs. These graphs are all related to each other and can help us understand the motion of an object.

Firstly, let's start with the displacement-time graph. This graph shows the change in an object's position over time. The slope of this graph gives us the velocity of the object at any given time. If the slope is positive, it means the object is moving in a positive direction (towards the right in your example graph) and if the slope is negative, it means the object is moving in a negative direction (towards the left in your example graph).

Next, let's look at the velocity-time graph. This graph shows the change in an object's velocity over time. The slope of this graph gives us the acceleration of the object at any given time. If the slope is positive, it means the object is accelerating in a positive direction (getting faster) and if the slope is negative, it means the object is accelerating in a negative direction (slowing down).

Finally, the acceleration-time graph shows the change in an object's acceleration over time. The slope of this graph tells us how the acceleration is changing over time. If the slope is positive, it means the acceleration is increasing (getting faster) and if the slope is negative, it means the acceleration is decreasing (slowing down).

Now, let's apply this to your example graph. The first section of the displacement-time graph shows a positive slope, meaning the object is moving in a positive direction and getting faster. This is reflected in the velocity-time graph with a positive slope, indicating the object is accelerating in a positive direction. The acceleration-time graph also has a positive slope, showing that the acceleration is increasing over time.

In the middle section of the displacement-time graph, there is a horizontal line. This means the object is not moving and has a velocity of 0. This is reflected in the velocity-time graph with a horizontal line at 0. The acceleration-time graph also has a horizontal line, indicating that the acceleration is constant and equal to 0.

In the final section of the displacement-time graph, there is a negative slope, meaning the object is moving in a negative direction and slowing down. This is reflected in the velocity-time graph with a negative slope, indicating the object is accelerating in a negative direction. The acceleration-time graph also has a negative