Question

Calculus again

Answer 1

@johnweldon1993

Answer 2

Sorry for the wait...1 sec :)

Answer 3

No problem ^_^

Answer 4

Okay so first thing is...we know what relationship between position and velocity?

Answer 5

umm. the relationship is that velocity is the final position minus the initial position over time?

Answer 6

Okay yes *trying to get something else but we'll work with that*

So what you're saying is

\[\large V = \frac{P_f - P_i}{t_f - t_i}\]

Right?

Answer 7

Right

Answer 8

Hmm...look familiar?

Hint*
\[\large m = \frac{y_2 - y_1}{x_2 - x_1}\]

It is the same as the slope right?

Answer 9

Mhm!

Answer 10

So we are basically proving that the velocity is the slope of the position at any given point

Well let me ask you...at t = 4....what does the slope LOOK like?

Answer 11

It looks like a horizontal line?

Answer 12

Is that the tangent?

Answer 13

Essentially we are looking for the slope at that 1 point

So yes we are basically putting a tangent line touching the graph at x = 4 and finding the slope of it

But since we dont have the equation of the graph...we just "guess-timate" it lol

At x = 4...going up to the graph...is there a positive or negative slope?

Answer 14

Negative?

Answer 15

Right, why dont you sound sure

Answer 16

It looked negative, I just couldn't prove it to myself. Now what do we do?

Answer 17

Lol i mean yeah it a subtle negative but still there

And from here we kinda just guess what the slope would be comparing to things we know

Likeeeee y = -2 does it seem comparable? orrrrr y = -4 what about that?

Answer 18

Where did you get y = -2 and y= -4 from? -4 seems to be the better match though

Answer 19

Look at your answer choices :)

Answer 20

Ohh. And since we already established that the slope is negative, it can't be A or D. I get it. So now we're just guessing between -2 and -4 okay cool

Answer 21

Right :)

Answer 22

So now...I mean obviously we cannot calculate it exactly...but I mean if we want to do a REAALLLLL rough estimate

It looks like at x = 4...we are at height = 9

and at x = 4.5 we look be to SOMEWHERE close to 8...so

\[\large V = \frac{8 - 9}{4.5 - 4} = \frac{-1}{.5} = -2\]

which is what I would have guessed at

Answer 23

Ohh. I see, okay. This one was weird, we weren't taught hot to do it xD

Answer 24

how*

Answer 25

Lol yeah these are annoying

I mean if you were given like y = -(x - 3)^2 + 10 for the equation *which actually might be right XDDD you could just differentiate it and solve for the slope at x = 4 exactly...but these happen sometimes lol

Answer 26

You were? I got -2 out of it after I got the derivative

Answer 27

Oh wow...yeah holy crap apparently I dont know how to do simple derivatives XDD

Answer 28

I did it then second guessed myself lol

Answer 29

XD Calc is so much fun cx

Answer 30

Lol I agree Cx

Alright but I'm headed out now...good luck with any other problems you have :)

Answer 31

Thanks! Thank you for your help ^_^