Are these motion diagrams of velocity & acceleration vectors correct?

[mileena]

Homework Statement

Draw motion diagrams for (a) an object moving to the right at constant speed, (b) an object moving to the right and speeding up at a constant rate, (c) an object moving to the right and slowing down at a constant rate, (d) an object moving to the left and speeding up at a constant rate, and (e) An object moving to the left and slowing down at constant rate. (f) How would your drawings change if changes in speed were not uniform; that is, if the speed were not changing at a constant rate?

Homework Equations

[none]

The Attempt at a Solution

Here is my answer, with drawings, in both .pdf and .odt (OpenOffice Writer, but you can also open it in Word) formats:

.pdf format:
http://bit.ly/15oXl9k

.odt format:
http://bit.ly/1497shy

Thank you!

 

[mfb]

Check your acceleration in (c). The object is slowing down.

(d) and (e): Which image comes first in the series? Based on that, are your diagrams right?

 

[mileena]

Thanks for the reply mfb.

See, I thought negative acceleration was to the left, and positive acceleration to the right. In fact, don't acceleration and velocity always have to agree in sign (either both positive or both negative), since they both use the same L (length) to determine this [while T (time) is always positive]? But my professor said acceleration could be perpendicular to velocity, meaning they would have opposite slopes with different signs.

By the way, in case anyone is wondering, I just uploaded the page from my textbook with motion diagrams, which seems to say I am wrong in the above. This has been very hard for me to learn.

http://bit.ly/18tMw0F

 

[mfb]

See, I thought negative acceleration was to the left, and positive acceleration to the right.

Okay

In fact, don't acceleration and velocity always have to agree in sign [...]?

No.
As an example, all objects in a free fall on Earth are accelerating downwards (towards the ground). Can objects move upwards in free fall? Sure, just throw something upwards.

But my professor said acceleration could be perpendicular to velocity, meaning they would have opposite slopes with different signs.

"Perpendicular" needs at least two dimensions, where "sign" is not a useful concept any more. You need vectors, and the relative orientations of those vectors can be anything.

 

[mileena]

Ok, thanks again. I just left the library, so I apologize for not being online for a while.

My understanding now is below, which very well likely is STILL wrong!

Positive acceleration means the object is increasing it magnitude of velocity (like when you accelerate your car after the traffic light turns green), whereas negative acceleration means the object is decreasing its magnitude of velocity (like when you slow down to a stop at a red light). Notice I said increasing or decreasing the magnitude of velocity, i.e., its absolute value, as the sign of the velocity (negative or positive) indicates direction, not magnitude of velocity or speed. So going from a velocity of -5 m/s to -10 m/s is a decrease in the overall velocity, but the object is actually speeding up, to the left.

All of the above is probably wrong!

Let me try to upload a revised doc in .odt format and in .doc format. (c) in the problem still seems right to me (even though I realize it's not), since the object is moving to the right and slowing down at a constant rate. I have the same size acceleration vector arrows pointing to the left, indicating negative acceleration; and I have increasingly smaller velocity vector arrows (indicating slowing down) pointing to the right (indicating motion to the right). I will try to draw it below (it is in the links below as well):

object is moving to the right and slowing down at a constant rate:

v: --------------> [biggest space] --------> [med. space] -----> [smallest space]-->

a: <--- <--- <--- <---

.odt format
http://bit.ly/1fr51GN

.doc format:
http://bit.ly/16ZNJPp

 

[mfb]

Positive acceleration means the object is increasing it magnitude of velocity

No. You always have to consider the direction.
Acceleration in one direction means the velocity in this direction increases. If the object happens to move in the other direction, this can be seen as "velocity in the opposite direction decreases".

Positive acceleration in one direction is negative acceleration in the other direction ;).

 

[mileena]

Ok, thank you mfb for posting again. I saw your post an hour ago, but I have been having a lot of difficulty figuring out positive and negative acceleration. Your post got me thinking again, and reinforced how wrong I was in my understanding. So I went to http://physicsclassroom.com/ for more help. They had the four combinations for velocity and acceleration (+v, +a; +v -a; -v +a; -v -a) with a motion diagram, position vs. time graph, velocity vs. time graph, and acceleration vs. time graph for each combination. I really had to study each one for a while, and then read a tip they posted:

If an object is slowing down, the the acceleration is always opposite the sign (i.e., direction) of the velocity. If it speeding up, the acceleration has the same sign as its velocity.

So positive velocity always means the object is going right or up.
Negative velocity means the object is going to the left or right.

But I am troubled by the fact that both positive acceleration and negative acceleration have no meaning. In other words, positive acceleration could mean either the object is speeding up (as with positive velocity) or slowing down (as with negative velocity). And positive acceleration could also mean either going rightward (as with positive velocity) or moving leftward (as with negative velocity). In short, positive acceleration, by itself, has no meaning! It is only meaningful in conjunction with velocity. The same with negative acceleration.

I hope this is right. This is why I became so confused. I wish our textbook had examples of each possible combination like the website above did. It would have helped me a lot!

 

[mileena]

No. You always have to consider the direction.
Acceleration in one direction means the velocity in this direction increases.

When you say "velocity in this direction increases", do you mean the magnitude of velocity is increasing, or the sign is now positive?

Regardless, the above is so true. I looked in the combination chart I just made, and of course, you are right. To rule out any ambiguity because of the English language, I am going to say: "Acceleration in one direction means the magnitude of the velocity, if it happens to be in this direction, increases in magnitude (absolute value, as opposed to mathematical sign) And if the velocity happens to be in the opposite direction as the acceleration, then the velocity decreases in magnitude (but not necessarily in mathematical sign).

Is the above correct? I hope?

If velocity is increasing, does that mean the object's direction is now rightwards or upwards; or does it mean the object is speeding up?

 

[mileena]

I just noticed something in the website I cited above:

http://www.physicsclassroom.com/mmedia/kinema/nvpa.cfm

For leftward movement (leftward velocity), they have their car going from right to left in their motion diagrams.

But I always go from left to right, even for leftward movement, since English is a left-to-write language. Should I change my motion diagrams?

 

[mileena]

Ok, I did revised motion diagrams. I think these are correct this time:

.odt format:
http://bit.ly/15jMrvA

.doc format:
http://bit.ly/14jrcK3

I am sorry I can't put these write here, but the spacing is all messed up if I do.

 

[mfb]

Now they are right.

You could make screenshots and add those images instead of the word documents.

 

[mileena]

Thank you! Finally. I hope I get it now. I can really dense at times. :)

And I completely forgot about doing screen shots. I thought about printing then scanning, but I don't have my printer as I am doing homework at a restaurant with wifi.