Which of the following could be the interpretation of the distance vs time graph shown?
Which of these answers this Question, Is It 1, 2, or 3 that's in parentheses???


( 1.) A biker takes off on a course that begins with a small ramp. The biker bikes up a hill and across a flat portion of the course before heading down a steep descent.

( 2.) A driver leaver her house and slows down to make a stop at her neighbor's house. She then drives at a constant speed and stops at a house further down the street. After visiting with her neighbor, she quickly drives back home.

( 3.) A hiker begins hiking, but shortly after realized he left his water bottle in his car. He turns around to get his water bottle and then starts hiking again at a constant rate. The hiker stops for lunch at the furthest point of his hike and then hikes back at a quicker constant rate.

Which Of The Following Could Be The Interpretation Of The Distance Vs Time Graph Shown?Which Of These

Answers

Answer 1

The slope of the curve is positive between the times t=0\text{ s}t=0 st, equals, 0, start a text, space, s, end text, and t=2 \text{ s}t=2 st, equals, 2, start a text, space, s, end text since the slope is directed upward. This means the acceleration is positive.

The slope of the curve is negative between t=2 \text{ s}t=2 st, equals, 2, start a text, space, s, end text, and t=8 \text{ s}t=8 st, equals, 8, start a text, space, s, end text since the slope is directed downward. This means the acceleration is negative.

At t=2\text{ s}t=2 st, equals, 2, start a text, space, s, end text, the slope is zero since the tangent line is horizontal. This means the acceleration is zero at that moment.

Concept check: Is the object whose motion is described by the graph above speeding up or slowing down at time t=4\text{ s}t=4 st, equals, 4, start a text, space, s, end text?

[Show me the answer.]

What does the area under a velocity graph represent?

The area under a velocity graph represents the displacement of the object. To see why to consider the following graph of motion that shows an object maintaining a constant velocity of 6 meters per second for a time of 5 seconds.

To find the displacement during this time interval, we could use this formula

\Delta x=v\Delta t=(6\text{ m/s})(5\text{ s})=30\text{ m}Δx=vΔt=(6 m/s)(5 s)=30 mdelta, x, equals, v, delta, t, equals, left parenthesis, 6, start text, space, m, slash, s, end text, right parenthesis, left parenthesis, 5, start text, space, s, end text, right parenthesis, equals, 30, start text, space, m, end text

which gives a displacement of 30\text{ m}30 m30, start text, space, m, end text.

Now we're going to show that this was equivalent to finding the area under the curve. Consider the rectangle of the area made by the graph as seen below.

The area of this rectangle can be found by multiplying the height of the rectangle, 6 m/s, times its width, 5 s, which would give

\text{ area}=\text{height} \times \text{width} = 6\text{ m/s} \times 5\text{ s}=30\text{ m} area=height×width=6 m/s×5 s=30 mstart text, space, a, r, e, a, end text, equals, start text, h, e, i, g, h, t, end text, times, start text, w, i, d, t, h, end text, equals, 6, start text, space, m, slash, s, end text, times, 5, start text, space, s, end text, equals, 30, start text, space, m, end text

This is the same answer we got before for the displacement. The area under a velocity curve, regardless of the shape, will equal the displacement during that time interval. [Why is this still true when velocity isn't constant?]

\text{area under curve}=\text{displacement}area under curve=displacementstart text, a, r, e, a, space, u, n, d, e, r, space, c, u, r, v, e, end text, equals, start text, d, i, s, p, l, a, c, e, m, e, n, t, end text

[Wait, aren't areas always positive? What if the curve lies below the time axis?]

What do solved examples involving velocity vs. time graphs look like?

Example 1: Windsurfing speed change

A windsurfer is traveling along a straight line, and her motion is given by the velocity graph below.

Select all of the following statements that are true about the speed and acceleration of the windsurfer.

(A) Speed is increasing.

(B) Acceleration is increasing.

(C) Speed is decreasing.

(D) Acceleration is decreasing.

Options A, speed increasing, and D, acceleration decreasing, are both true.

The slope of a velocity graph is the acceleration. Since the slope of the curve is decreasing and becoming less steep this means that the acceleration is also decreasing.

It might seem counterintuitive, but the windsurfer is speeding up for this entire graph. The value of the graph, which represents the velocity, is increasing for the entire motion shown, but the amount of increase per second is getting smaller. For the first 4.5 seconds, the speed increased from 0 m/s to about 5 m/s, but for the second 4.5 seconds, the speed increased from 5 m/s to only about 7 m/s.

Example 2: Go-kart acceleration

The motion of a go-kart is shown by the velocity vs. time graph below.

A. What was the acceleration of the go-kart at time t=4\text{ s}t=4 st, equals, 4, start a text, space, s, end text?

B. What was the displacement of the go-kart between t=0\text{ s}t=0 st, equals, 0, start text, space, s, end text and t=7\text{ s}t=7 st, equals, 7, start text, space, s, end text?

A. Finding the acceleration of the go-kart at t=4\text{ s}t=4 st, equals, 4, start a text, space, s, end text

We can find the acceleration at t=4\text{ s}t=4 st, equals, 4, start a text, space, s, end text by finding the slope of the velocity graph at t=4\text{ s}t=4 st, equals, 4, start a text, space, s, end text.

\text{slope}=\dfrac{\text{rise}}{\text{run}}slope=  

run


Related Questions

Help me plsssssssssssssssssssssssssss

Answers

Shshshsha wowowow okk 728

Answer: 37 cm^2

Step-by-step explanation:

Break the shape into two recognizable shapes. In this case a triangle and a square. To find area of a triangle use Area= 1/2 base x height. To find area of a square use Area = length x width. Then add the two together.

Can you round 14.392

Answers

Answer:

The answer would be 14.0

Step-by-step explanation:

you would find what the decimal is and because it is below 14.49 you would round down

Please mark as brainllest i really need it have a nice week  

[o]-[o]

\___/

Please anyone ?? Helpp

Answers

Answer:

Does this count as stander form 6.95880148018

Step-by-step explanation:

HELP ME PLS I REALLY NEEDD HELP!!!! MATH IS HORRIBLE


pls number them like

1.

2

3.

4.

5.






help!
lol

Answers

Answer:

Question 1

Option 2 is the correct answer

y = x - 55/ x=255

Question 2:

Last option is the correct answer

n = b + 2/ b= 5

Step-by-step explanation:

Question 1

The given information can be framed into the Mathematical form as given below:

No of cards = x

Cards given to brother = 55

Remaining cards = x - 55

Total number of cards = y

y = x - 55

Plug y = 200

200 = x - 55

20. + 55 = x

x = 255

y = x - 55/ x = 255

Question 2:

Total number of shirts bought

n = b + 2

Plug n = 7

7 = b + 2

7 - 2 = b

b = 5

n = b + 2/ b = 5

Which equation represents a line passing through the point (8, 9) with a slope of 3?

Answers

The equation of a line passing through the point (8, 9) with a slope of 3 is y = 3x - 15.

What is the equation of a line passing through two given points in 2-dimensional plane?

Suppose the given points are [tex](x_1, y_1) and (x_2, y_2),[/tex]

then the equation of the straight line joining both two points is given by

[tex](y - y_1) = \dfrac{y_2 - y_1}{x_2 - x_1} (x -x_1)[/tex]

We have been given a line passing through the point (8, 9) with a slope of 3.

then the equation of the straight line joining both two points is given by

[tex](y - y_1) = \dfrac{y_2 - y_1}{x_2 - x_1} (x -x_1)[/tex]

Its slope would be:

[tex]m = \dfrac{y_2-y_1}{x_2-x_1}[/tex]

m = 3

Therefore, the equation of the straight line

[tex](y - 9) = 3 (x -8)\\\\y - 9 = 3x - 24\\\\y = 3x -15[/tex]

Hence, the equation of a line passing through the point (8, 9) with a slope of 3 is y = 3x - 15.

Learn more about straight-line equations here:

https://brainly.com/question/380976

#SPJ2

I need help with it ​

Answers

Answer:

variable, variable, known, unknown

Step-by-step explanation:

A shipping and handling free 35.00 is charged to all furniture over $250 if the order is $437.50 what percent is the shipping and handling free?

Answers

Answer:

8%

Step-by-step explanation:

Divide 35 and 437.50 and you get 0.8

Then multiply .8 times 100 = 8%

the other person is correct give brainliest

24 is what percent of 60​

Answers

Answer: 14.4

Step-by-step explanation:

60 * (24/100) = 14.4

Jean junction is selling jeans at 12% off the regular price. The regular price is $32.00 per pair. What is the discount amount

Answers

Discount amount is 3.75 I think!

Beginning: Identify 3 ordered pairs that are solutions to the inequality:
1st Ordered Pair
2nd Ordered Pair
3rd Ordered Pair
Submit

Answers

Answer:

what are the ordered pairs?

Trigonometry help finding the value of x

Answers

Answer:

[tex]5\sqrt{3}[/tex] or 8.66

Step-by-step explanation:

use tan:

tan = [tex]\frac{opposite}{adjacent}[/tex]

⇒ tan 60 = [tex]\frac{x}{5}[/tex]

tan of 60 is 1.73

⇒ 1.732 = [tex]\frac{x}{5}[/tex]

multiply 5 on both sides

⇒ 1.732 x 5 = [tex]\frac{x}{5}[/tex] x 5

⇒ 8.66

Answer:

[tex]\boxed {\boxed {\sf D. \ 5 \sqrt 3 \ or \ 8.66}}[/tex]

Step-by-step explanation:

Remember the 3 main trigonometric ratios:

sinθ= opposite/hypotenuse cosθ= adjacent/hypotenuse tanθ= opposite/adjacent

We are given the 60 degree angle. 5 is adjacent to the angle and x is opposite. Therefore, we must tangent.

[tex]tan \theta= \frac {opposite}{adjacent}[/tex]

[tex]tan60=\frac {x}{5}[/tex]

Since we are solving for x, we must isolate that variable. It is being divided by 5 and the inverse of division is multiplication. Multiply both sides by 5.

[tex]5(tan60)=\frac {x}{5} *5[/tex]

[tex]5(tan60)=x\\5*$$1.73205080757= x\\8.66025403784=x[/tex]

If we round to the nearest hundredth, the 0 in the thousandth place tells us to leave the 6.

[tex]8.66 \approx x[/tex]

x is about 8.66 or 5√3, which is choice D.

Da Baby has $45,000 and earns $2,500 each hour
from streams. JoJo Siwa has $62,000, earns $2,000
each hour from streams.
How
SI
Each equation represents the amount in the bank after
t hours.


Da Baby: s= 2,500t + 45,000
JoJo Siwa: s= = 2,000t + 62.000
How many hours, will it take for Da Baby and JoJo
Siwa to have the same amount in the bank?

Answers

Answer:

Step-by-step explanation:

maybe 30 vtfyubf6tyubtfcgnfgghghnvb ngvbhfhgbfvgn

Help I’ll give out brainliest pls dont answer if you don’t

Answers

Answer:

8x-8=16 is the answer after combining like terms

Answer:

x=3

Step-by-step explanation:

8x-8=16

8x=24

x=3

:)

add my sc tregan_fought

Answers

are you old???????????

please help with explanation and show work :)

Answers

3. A=bh/2
2A=bh
h=2A/b.

8. Dy-Cx=E
Dy=E+Cx
y=(E+Cx)/D

if the temperature at the North Pole is -10º F, how many degrees would the temperature have to increase for it to be 0º?

Answers

Answer:

10 degrees

Step-by-step explanation:

:) Thank you enjoy your day kind human :)

Answer:

10.

Step-by-step explanation:

-10 + 10 = 0.

works the same for degrees as well.

what is the area of circle if diameter is 6feet

Answers

Answer:

Area=πr²

=3.14×(6/2)²

=28.26 ft²

Step-by-step explanation:

M is directly proportional to R cubed a)R = 4, M = 160 find M when R = 2 b) work out the value of R when M=540

Answers

Answer:

a k (proportionality constant) = 2.5

b. r = 6

Step-by-step explanation:

Here, we want to solve a variation

m = k * r^3

160 = k * 4^3

160 = 64k

k = 160/64

k = 2.5

b) secondly;

From;

540 = 2.5 * r^3

r^3 = 216

r = cube root of 216

r = 6

a function may assign the same output value to two different input values

Answers

this is true i i i i i i i i i i i i

A study was conducted to investigate whether the mean price of a dozen eggs was different for two different grocery stores, Store A and Store B, in a large city. A carton of one dozen eggs from each store was randomly selected for each of 35 weeks, for a total sample size of 35 cartons from each store. The mean price of the 35 cartons was recorded for each store. The difference in the mean carton price for the stores will be calculated.

Which of the following is the appropriate test for the study?

A one-sample z -test for a population proportion

A one-sample t -test for a sample mean

A matched-pairs t -test for a mean difference

A two-sample t-test for a difference between population means

A two-sample z-test for a difference between population proportions

Answers

Answer:

A two-sample t-test for a difference between population means

Step-by-step explanation:

Answer:

D) A two-sample  t -test for a difference between population means

Step-by-step explanation:

Two random samples are selected on a quantitative variable, and the difference in the sample means will be calculated. The appropriate test is the two-sample t-test for a difference in population means.

Bob made $209 for 11 hours of work.
At the same rate, how much would he make for 13 hours of work?

Answers

Answer:

He would make $247

Step-by-step explanation:

have a great day!

Please help need the answer now!!

Answers

Answer:

The answer would be D

Step-by-step explanation:

In order for a problem to be infinite, it must be 0=0. But since this is equal, and can equal 0=0, it would be d

please help me, i'll mark you brainiest
20 points

Answers

Answer: 4! 300:75     Hope you have a great day! Good luck on any stressful school homework stuff you have today too!

Step-by-step explanation: A fraction consists of two numbers and a fraction bar:

300/75

The number above the bar is the numerator: 300

The number below the bar is the denominator: 75

Divide the numerator by the denominator to get fraction's value:

300/75 =

300 ÷ 75 =

4:1

help pls ill mark best answer brainliest

Answers

Answer:d= 19

Step-by-step explanation:

Two linear functions are shown.
Which function has the greater
initial value?
Function B
y = 6x + 3
Function A
Х y
- 1 9
0 6
1 3
2 0
Function has the greater initial value because the initial value for Function A is and the initial
value for Function B is
(Type integers or decimals.)
Enter your answer in the edit fields and then click Check Answer.
All parts showing

Answers

Answer:

Function A has a greater initial value because the initial value for Function A is 6 and the initial vale for Function B is 3

Step-by-step explanation:

The data for Function A is presented here as follows;

[tex]\begin{array}{cc}x&y\\-1&9\\0&6\\1&3\\2&0\end{array}[/tex]

The slope of the function, 'm', is given using any two points as follows;

m = (9 - 3)/((-1) - 1) = -3

The slope of the function = -3

The equation of function in point and slope form is given as follows;

y - 3 = -3·(x - 1)

The equation of Function A, is therefore, given as follows;

y = 3 - 3·x + 3 = 6 - 3·x

∴ y = 6 - 3·x

The equation of Function B is given as follows;

y = 6·x + 3

The initial value of a function is given by the y-intercept of the function, where the input variable (x-variable) is zero

The initial value, (y-intercept) of Function A, f(0) is therefore found as follows;

f(x) = y = 6 - 3·x

f(0) = 6 - 3×0 = 6

The initial value of Function A, f(0) = 6

Similarly, the initial value, (y-intercept) of Function B, f(0) is found as follows;

f(x) = y = 6·x + 3

f(0) = 6×0 + 3 = 3

The initial value of the Function B, f(0) = 3

Therefore, we have that Function A has a greater initial value than Function B

Find the smallest number such that the remainder is 3 when it is divided by 16,20 or 24.​
(step required,thank you)

Answers

Answer: 123

Step-by-step explanation:

Foe us to solve this, we have to find the lowest common multiple of 16, 20 and 24 first and then add 3 to the LCM. This goes thus:

Multiples of 16 = 16, 32, 48, 64, 80, 96, 112, 128, 144, 160

Multiples of 20 = 20, 40, 60, 80, 10, 120, 140, 160

Multiples of 24 = 24, 48, 72, 96, 120

Therefore, the Lowe's common multiple is 120.

We then add the remainder of 3 and this will give:

= 120 + 3

= 123

please please complete it ​

Answers

Answer:

1. 14

2. 11

3. 19.5

4. 16

5. 76

6. 10

7.  2.5

8. 4.5

9. Mean: 10, Median: 9, Mode: 7

10. Mean: 6, Median: 7, Mode: 8,5

11. Mean: 10, Median: 11.5, Mode: 12

Step-by-step explanation:

May someone please help me with this :)

Answers

1. The perimeter = 3.7 + 3.7 + 2.8 + 2.8
= 13
The area = 3.7 * 2.8 = 10.36

2. Perimeter = 11.2
Area = half base times height
2.6 * 1.5 = 3.9 squared
Do you got the answer?

find the value of x in each triangle with the given angle measures ​

Answers

Answer:

10 - 104

11 - 25

12 - 64

13 - 109

14 - 33

15 - 90

Step-by-step explanation:

For the first 3 triangles u must add the two angles and minus it from 180

Q number 13 do the same thing then minus the number u got by 180

Q number 14 .... 66 - 180 = 33

Q number 15 it is a right angle so it is 90

what is the volume???

Answers

Answer:

that would be 80

Step-by-step explanation:

Here it is

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