Is the velocity of this object increasing or decreasing?

[TMalan]

Homework Statement

Hi everyone,
8th grade physics teacher here.

We are doing a handout where we have to identify time-velocity graphs with descriptions. Can you help me with this one?

https://imgur.com/a/vEIkg

A) The velocity is increasing at a uniform rate.
B) The velocity is decreasing at a uniform rate.

Homework Equations

The Attempt at a Solution

[/B]
At first I thought it was decreasing but then an 8th grade student said 1) the slope is positive and 2) if you continue the line after the x-axis it will be increasing. Also, the Vf is literally higher on the y-axis than Vi.dd

I think the same question could be raised about displacement that is negative but with a positive slope approaching the x-axis. The displacement on the y-axis would be going up, but it is decreasing since it's getting closer to the starting point.

Let me know your thoughts!

 

[Curiosity 1]

The velocity is increasing at an uniform rate. When we talk about the rate of change of velocity, we are talking about acceleration. Acceleration is just the slope (dv/dt) of the velocity graph. From the graph, the velocity is obviously increasing with time, and since the graph is a straight line, its derivative (dv/dt) will be constant (uniform rate), so we call it increasing at an uniform rate

 

[Curiosity 1]

Since the question didn't specify where the velocity is respect to... For the sake of example, let's just assume the velocity is positive if the object moves in +x direction, and negative otherwise. Then from the graph, the starting velocity (at t=0) is let's say -5m/s, so the object is moving at speed of 5m/s to -x direction. "Scanning" across the graph, we can see that the velocity is becoming less negative as time increases. Less negative means the velocity is increasing (take a point that is higher in the graph minus a point lower in the graph is positive). What does this mean in turn? It's just mean the object is moving at slower speed in the -x direction! When the graph intersects the x-axis, the velocity is zero, so the object stops. In short, the object moves in -x direction, and its speed becomes slower and slower over the time until the speed is zero. Hope this helps!

 

[TMalan]

It does! Thank you!

 

[PeroK]

The Attempt at a Solution

At first I thought it was decreasing but then an 8th grade student said 1) the slope is positive and 2) if you continue the line after the x-axis it will be increasing. Also, the Vf is literally higher on the y-axis than Vi.dd

I think the same question could be raised about displacement that is negative but with a positive slope approaching the x-axis. The displacement on the y-axis would be going up, but it is decreasing since it's getting closer to the starting point.

Let me know your thoughts![/B]

Velocity is increasing. Speed, the magnitude of velocity, is decreasing while velocity is less than 0 and increasing thereafter.

Displacement is a different matter. When velocity is negative, the change in displacement is negative, so displacement decreases until the velocity reaches 0, after which displacement increases.

Note that, although perhaps not something to get into at this level, the concept of velocity (and displacement) increasing or decreasing is only really valid for one dimensional motion. In 2D or 3D motion, you can't directly compare velocities in this way. In these cases, you are more likely to look at whether the speed or distance from the origin is increasing and decreasing.

In your example, of course, if you consider speed and distance from the starting point, then you get a very different analysis.