anonymous
  • anonymous
Find the average velocity of the object from points A to B, B to C , and A to C .
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
|dw:1328486272548:dw|
anonymous
  • anonymous
the points are a(0)=0 B(3)=25 c(6)=0
anonymous
  • anonymous
My answer was 8.33,7, and zero

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anonymous
  • anonymous
i mean -7
anonymous
  • anonymous
Average velocity is given by [f(b)-f(a)]/b-a. So, for the first part, you'd want to do [f(3)-f(0)]/3-0
anonymous
  • anonymous
i did that
anonymous
  • anonymous
Then what is your question?
anonymous
  • anonymous
my answer is wrong
anonymous
  • anonymous
can you solve for it and tell me if our answers match up
anonymous
  • anonymous
Yes
anonymous
  • anonymous
Okay. What I get is this: [25-0]/[3] = 8.333 That should be correct. Next, [f(6)-f(3)]/(6-3) = (0-25)/3 = -8.333 And lastly: [f(6)-f(0)]/(6-0) = (0-0)/6 = 0
anonymous
  • anonymous
why is the second one 8.33
anonymous
  • anonymous
ohh i apologize you are right thank you
anonymous
  • anonymous
Well, a good way to look at this visually is to look at the graph: I'm assuming that that parabola is symmetrical. The curve comes up at the average velocity (slope) of 8.333. Then it comes back down with a similar slope, but negative. Hence the -8.333
anonymous
  • anonymous
Oh, good! I'm glad!
anonymous
  • anonymous
can you also help me with this For the intervals in above would the average speed be less than, equal to, or greater than the values you found in that Part?
anonymous
  • anonymous
Yes, let me think for a moment.
anonymous
  • anonymous
Well, speed is different from velocity in the fact that velocity has direction. For example, the answer we got from A to B and B to C were the same except for their sign, right? That's because velocity is specific to the direction. A to B was going up, B to C was going down. Speed doesn't have that distinction. If you were to take the average speed from A to B, it'd be the same, but from B to C, speed doesn't care about direction; it would be 8.333 without the negative. Does that help?
anonymous
  • anonymous
so speed and velocity are the same magnitude but speed doesnt have direction . so speed tells you how fast you are going but not where you going
anonymous
  • anonymous
Yes! So do you think the average speed from B to C would be greater than, equal to, or less than the average velocity from B to C?
anonymous
  • anonymous
i think it would be greater
anonymous
  • anonymous
I would agree :)
anonymous
  • anonymous
how about from ac
anonymous
  • anonymous
As far as I know, there would be no change from average velocity to average speed.
anonymous
  • anonymous
the answer choices has one of the them stay equal and the other 2 be greater
anonymous
  • anonymous
Could you list the available choices? Thanks.
anonymous
  • anonymous
yah equal for ab, greater for bc, ac equal for bc, greater for ab ac equal for ac greater for ab ac
anonymous
  • anonymous
Huh. One moment.
anonymous
  • anonymous
yah i know
anonymous
  • anonymous
Oh. Okay. I think I know. So, we said that the velocity from A to B was 8.333, right? And we said that the velocity from B to C was -8.333. If you wanted to find the average for the entire thing, you would do (8.333+[-8.333])/2. Make sense? You just add them (because they cover the entire graph and divide it to find average. Now, let's look at speed. We decided that from A to B stayed the same: 8.333, but we also decided that B to C changed to 8.333. Let's take the average:
anonymous
  • anonymous
(8.333+8.333)/2. This is the average from A to C! And it's greater with speed than it is velocity! That answers our question, I think. Same for AB, but greater for BC and AC.
anonymous
  • anonymous
Did you follow that?
anonymous
  • anonymous
kinda of im a little confused to be honest
anonymous
  • anonymous
Okay. Let's see if I can clear this up.
anonymous
  • anonymous
The average velocity of the entire curve can be obtained by adding together the avg velocity of one half of the curve and the other half and then dividing it by 2. Does that make sense?
anonymous
  • anonymous
yah
anonymous
  • anonymous
Okay, and the average velocity for the entire curve is the same thing as average velocity from A to C, yes?
anonymous
  • anonymous
yah bevause the entire curve goes from a to c
anonymous
  • anonymous
Our velocity: \[[8.333+(-8.333)]\div2\] Our speed: [8.333+8.333]div2 Do you see and understand the difference?
anonymous
  • anonymous
Oops.\[[8.333+8.333]\div2 \]
anonymous
  • anonymous
yah our velocity is zero and our speed is somethings else
anonymous
  • anonymous
so it shows that it changed?
anonymous
  • anonymous
Right! And did it become greater than or less than? What do you think?
anonymous
  • anonymous
it became greater
anonymous
  • anonymous
Yes. So, in conclusion, we agreed that AB is the same, BC is greater and just now, AC is also greater. Is that an option?
anonymous
  • anonymous
yah you are right it is correct. so when we have tofind speed we have to always find the average
anonymous
  • anonymous
Well, at this point, if you do not have a function for speed, you can only 'guess'. In Calculus it is possible to find the instantaneous speed, but otherwise you can only take averages.
anonymous
  • anonymous
can you explain quickly how you find the average of anything
anonymous
  • anonymous
Well, you add up all of the terms (whatever they may be) and then divide it by the number of terms. Good?
anonymous
  • anonymous
but didnt we have 3 terms
anonymous
  • anonymous
No, we had 1 half of the curve and the other half of the curve, so we divided by two, right?
anonymous
  • anonymous
okay . sohow do we know if we have a function for speed
anonymous
  • anonymous
Well, in the example you were just given a position function; the graph showed the position of the object over time. If the question had included a v(t) function, i.e. velocity over time, you could use it to find the velocity. Or, if the question had included a s(t) function, speed over time, you could use it to find the speed. Neither of these were included so we don't worry about it.
anonymous
  • anonymous
so just as a refresher what is a function
anonymous
  • anonymous
In general (and by no means is this an all inclusive definition) it is an equation that you put in an input (typically x) and receive and output (typically y). It has to pass the 'vertical line test' meaning that there are no two x values that equal the same y value.
anonymous
  • anonymous
okay thank you for all your help and patience.
anonymous
  • anonymous
You're welcome :) Good luck!
anonymous
  • anonymous
thanks.

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