# Kinematics Graphical Argument

Quick question about translating what's on the Velocity vs Time graph into what is actually happening to the object. A cart is traveling on a straight horizontal track. So I determined that east is positive direction. So, if the velocity vs time graph is showing a negative slope of -0.2 does that mean that the cart is going backwards due west? (Vise versa, If cart has positive slope it is going forward?) If not what is the cart actually doing?

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Nathanael
Homework Helper
If the value of the velocity-time graph were -0.2, then it would be going backwards.

The slope of the velocity-time graph represents the acceleration of the object (in this case, it's slowing down).

What do you mean the value? The line's starting position is at 9seconds on the velocity of -1.0. It has a positive slope of 0.2 and stops at 12seconds at -0.4. So this line is under the 0 line. So if it is under the line, with a positive slope what does that mean?

Nathanael
Homework Helper
°By "value" I mean the "y-coordinate" a.k.a. the height of the graph. (Sorry, I can't think of a better way to say it.)

So if the height of the graph is negative, (in other words, if the graph is below the time axis) then the velocity is in the negative direction (a.k.a. "backwards")

If the slope is positive, that means there is acceleration in the positive ("forwards") direction. If the slope is negative, then the acceleration is in the "backwards" direction. If the slope is zero, then there is no acceleration.

To summarize:
The height of the graph is the velocity, and the slope of the graph is acceleration.

What do you mean the value? The line's starting position is at 9seconds on the velocity of -1.0. It has a positive slope of 0.2 and stops at 12seconds at -0.4. So this line is under the 0 line. So if it is under the line, with a positive slope what does that mean?
The direction of the slope (either positive or negative) tells you the direction of the acceleration.

So if you're moving in the positive direction with a positive slope, then you will be speeding up
(you will be increasing your speed in the positive direction)

If you're moving in the negative direction with a negative slope, then you will still be speeding up
(but you will be increasing your speed in the negative direction)

If you're moving in the positive direction with a negative slope (or if you're moving in the negative direction with a positive slope) then you will be slowing down.

To summarize:
If the graph is sloping towards the "zero line" then you are slowing down.
If it is sloping away from the zero line, you are speeding up.
"Positive" and "negative" are just directions.

Thanks a lot :) I got it now. I was mainly confused on what was happening below the x axis. But now I understand that when the line has a negative slope under the x axis, the object is moving backwards faster vs. positive slope, the object is slowing down!