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the points are a(0)=0 B(3)=25 c(6)=0
My answer was 8.33,7, and zero
i mean -7
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
i did that
Then what is your question?
my answer is wrong
can you solve for it and tell me if our answers match up
Okay. What I get is this: [25-0]/ = 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
why is the second one 8.33
ohh i apologize you are right thank you
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
Oh, good! I'm glad!
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?
Yes, let me think for a moment.
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?
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
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?
i think it would be greater
I would agree :)
how about from ac
As far as I know, there would be no change from average velocity to average speed.
the answer choices has one of the them stay equal and the other 2 be greater
Could you list the available choices? Thanks.
yah equal for ab, greater for bc, ac equal for bc, greater for ab ac equal for ac greater for ab ac
Huh. One moment.
yah i know
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:
(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.
Did you follow that?
kinda of im a little confused to be honest
Okay. Let's see if I can clear this up.
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?
Okay, and the average velocity for the entire curve is the same thing as average velocity from A to C, yes?
yah bevause the entire curve goes from a to c
Our velocity: \[[8.333+(-8.333)]\div2\] Our speed: [8.333+8.333]div2 Do you see and understand the difference?
yah our velocity is zero and our speed is somethings else
so it shows that it changed?
Right! And did it become greater than or less than? What do you think?
it became greater
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?
yah you are right it is correct. so when we have tofind speed we have to always find the average
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.
can you explain quickly how you find the average of anything
Well, you add up all of the terms (whatever they may be) and then divide it by the number of terms. Good?
but didnt we have 3 terms
No, we had 1 half of the curve and the other half of the curve, so we divided by two, right?
okay . sohow do we know if we have a function for speed
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.
so just as a refresher what is a function
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.
okay thank you for all your help and patience.
You're welcome :) Good luck!