Question

I have a multiple question promlem could someone please help me with it

Answer 1

Instructions:The following table gives the velocity in the vertical direction(in ft/sec) of a rider on a Ferris Wheel at an amusement park. (A positive velocity means the rider is going up.) The time,t, is measured in seconds after the ride starts. The table gives the values for one complete revolution of the wheel.

Answer 2

Table:

Answer 3

Question 1: During what interval of time is a(t), the acceleration of the rider, negative? Give a reason for your answer.
Question 2: What is the average of a(t), the acceleration of the rider, during the first 15 seconds of the ride? Include units of measure.
Question 3: Approximate\[\int\limits_{0}^{30}v(t)dt\] using a right hand Riemann sum with six intervals of equal length.
Question 4:What does the equationin question 3 tell about the Ferris Wheel?

Answer 4

@tcarroll010 can you help me figure out these problems please.

Answer 5

@smokeydabear can you help me with these problems plese

Answer 6

The first question is asking when the acceleration is negative. The acceleration will be negative when the velocity is decreasing, and positive when it is increasing. Can you tell me what you think the time interval is now?

Answer 7

35-50 seconds

Answer 8

The 50 second part is right, but look closer for the first end. When does the velocity start decreasing?

Answer 9

Oh and nvm, it should be 45 sec not 50 sec.

Answer 10

30-45

Answer 11

Try again, velocity can be positive and still decreasing.

Answer 12

15-45

Answer 13

Yep! Now tell me in your own words why that interval has negative acceleration.

Answer 14

because it starts decreasing and which meand that the negative when the velocity is decreasing

Answer 15

Sounds good to me ^^ So now the next question is asking for the average acceleration during the first 15 seconds. Do you have any ideas on how to find the average acceleration?

Answer 16

no

Answer 17

You can try to section it off from the rest of the graph and just look at all the values from 0-15 seconds. How much does the speed change in that time?

Answer 18

I have no idea

Answer 19

Speed is just another word for velocity for all intents and purposes here. How much does v(t) change by in 15 seconds?

Answer 20

changes by 7.4

Answer 21

Are you adding all the velocities up? Just take the difference between the starting velocity and the final velocity, and you have 3.1-0=3.1. Make sense?

Answer 22

oh ok I totally was confussed I understand now

Answer 23

So now you want to take that change in velocity and divide it by the change in time. What do you get?

Answer 24

3.1/15=.206

Answer 25

Yep, and that is your average acceleration for that time interval.

Answer 26

The question wants you to include units of measure, so the acceleration would be .206 ft/sec^2

Answer 27

ok got it

Answer 28

The third question wants you to approximate the integral of v(t) using a Riemann's sum (specifically the right hand side). Riemann's sum is used to approximate integrals in any case by filling in the graph with rectangles that you can easily take the area of and adding up all of their sums. Let me refresh my memory really quick and I'll get back to you.

Answer 29

ok

Answer 30

Okay so it wants us to do Riemann's Sum using 6 partitions, meaning 6 rectangles to estimate the area under the curve. The interval we are looking at is 0-30, so we need to split that up into 6 equal parts. How big would those parts be?

Answer 31

2

Answer 32

Think about it like this. You have a long bar of chocolate that is split into 30 pieces (imagine how Hershey's bars look). Now you need to split that up and give an equal number to 6 people. How many individual pieces would everyone get?

Answer 33

5

Answer 34

Yep, so we will be splitting up this integral into 6 pieces that are 5 units long each:

0-5
5-10
10-15
15-20
20-25
25-30

The problem specifically asks that we use the right hand side to form our rectangles, so the heights will be according to the right-most point in each interval:

For the 0-5 segment, we will determine the height of the rectangle using 5 as our arbitrary x value. What is the function equal to when x=5 (Essentially, what is the speed at 5 seconds)?

Answer 35

1.6

Answer 36

Exactly, so the height of this rectangle will be 1.6 units, while its width will be 5 (because we already determined that each segment has the same width of 5). What is the area of this rectangle?

Answer 37

that is when I become confused

Answer 38

You are simply finding the area of a rectangle whose width is 5 and length is 1.6:

L x W = A, where L = 1.6 and W = 5

Answer 39

8 area

Answer 40

Exactly! That is all we need to know about the first rectangle. Now the second rectangle, which is from 5-10, needs to be evaluated in the same way. Do you think you can handle this one?

Answer 41

4.3*5=21.5

Answer 42

Where did you get the 4.3 from? Remember that you have to use the right-hand side (x=10) to find the height.

Answer 43

Oh I see what you did, do not add the velocities up, just do them individually.

Answer 44

oh 2.7*5=13.5

Answer 45

Very good! Second rectangle is down, four more to go. Wanna do the next one by yourself?

Answer 46

3.1*5-=15.5

Answer 47

Yep, now do the next three and show me what you got for each of them.

Answer 48

2.7*5=13.5 1.6*5=8 0*5=0

Answer 49

Yeah, now all we have to do is add all the areas up, and that's it for Riemann's sum.

Answer 50

ok so you get 58.5

Answer 51

Yep, and that is the approximate area under the graph of v(t). Integration of a line is simply finding the area under that line, if you can picture that. Riemann's sum estimates that, so the actual integral will be very close to 58.5. But you only needed to do Riemann's sum, so that's it for question 3.

Answer 52

ok so qwhat is 4

Answer 53

It is asking what the equation in question 3 says about the ferris wheel. In case you didn't know already, the integral of the velocity function v(t) is simply the equation for position. You can use the position function to find exactly where the object is after a given amount of time. So the integral of v(t) can be used to see how high you are at a given time.

Answer 54

Does this all make sense now?

Answer 55

yes thank you

Answer 56

I am glad I could help another person with math, I know how it feels to be in your situation. Try to understand concepts over formulas and the formulas will just fall in place, I assure you.