A vehicle moves along a straight road. The vehicle's position is given by f(t), where t is measured in seconds since the vehicle starts moving. During the first 10 seconds of the motion, the vehicle's acceleration is proportional to the cube root of the time since the start. Which of the following differential equations describes this relationship, where k is a positive constant?

a. df/dt= k3√t
b. df/dt= k3√f
c. d^2f/dt^2= k3√t
d. d^2f/dt^2= k3√f

Answers

Answer 1

Answer:

C. [tex]\frac{d^{2}f}{dt^{2}} = k\cdot \sqrt[3] {t}[/tex]

Step-by-step explanation:

Physically speaking, the acceleration is equal to the second derivative of the position of the vehicle in time. After a careful reading to the statement, we construct the following ordinary differential equation:

[tex]\frac{d^{2}f}{dt^{2}} = k\cdot \sqrt[3] {t}[/tex]

Where:

[tex]t[/tex] - Time, measured in seconds.

[tex]k[/tex] - Proportionality constant, measured in meters per second up to 7/3.

Therefore, the correct answer is C.

Answer 2

The differential equation that models the situation is:

[tex]\frac{d^2f}{dt^2} = k\sqrt[3]{t}[/tex]

Which is option C.

The position is the integral of the acceleration, with is the integral of the acceleration, hence, the relation between the position and the acceleration is:

[tex]\frac{d^2f}{dt^2}[/tex]

The acceleration is proportional to the cube root of the time since the start, hence:

[tex]\frac{d^2f}{dt^2} = k\sqrt[3]{t}[/tex]

In which k is the constant of proportionality.

A similar problem is given at https://brainly.com/question/14480252


Related Questions

In planning her​ retirement, Liza deposits some money at 4​% ​interest, with twice as much deposited at 4.5​%. Find the amount deposited at each rate if the total annual interest income is ​$2080.

She deposited ​$___ at 4​% and ​$____ at 4.5%.

Answers

She deposited $16,000 at 4% and $32,000 at 4.5%

She deposited $16,000 at 4% and $32,000 at 4.5%.

Let's assume Liza deposited an amount x at 4% interest. According to the given information, she deposited twice as much, which is 2x, at 4.5% interest.

To calculate the interest income from the deposits, we'll use the formula: Interest = Principal × Rate × Time.

At 4% interest, the interest earned is 0.04x (4% expressed as a decimal multiplied by x).

At 4.5% interest, the interest earned is 0.045(2x) (4.5% expressed as a decimal multiplied by 2x).

We know that the total annual interest income is $2080. Therefore, we can write the equation:

0.04x + 0.045(2x) = 2080

Simplifying the equation:

0.04x + 0.09x = 2080

0.13x = 2080

x = 2080 / 0.13

x ≈ 16,000

Liza deposited approximately $16,000 at 4% interest, and since she deposited twice as much at 4.5% interest, she deposited approximately $32,000 at 4.5% interest.

Therefore, she deposited $16,000 at 4% and $32,000 at 4.5%.

To know more about deposited:

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Mikhael wanted to rewrite the conversion factor "1 yard ≈ 0.914 meter" to create a conversion factor to convert meters to yards. Complete the explanation to tell how Mikhael should finish his conversion. If necessary, round to three decimal places.


(select)
1 yard by 0.914 m gives the rate of yards per meter. So 1 meter ≈
yards.
plz need help

Answers

Answer:

[tex]1\ meter = 1.094\ yard[/tex]

Step-by-step explanation:

Given

[tex]1\ yard = 0.914\ meter[/tex]

Required

Create a convert meter to yard expression

[tex]1\ yard = 0.914\ meter[/tex]

Divide both sides by 0.914

[tex]\frac{1\ yard}{0.914} = \frac{0.914\ meter}{0.914}[/tex]

[tex]\frac{1\ yard}{0.914} = 1\ meter[/tex]

[tex]1.09409190372\ yard = 1\ meter[/tex]

[tex]1\ meter = 1.09409190372\ yard[/tex]

[tex]1\ meter = 1.094\ yard[/tex] --- approximated

Answer:

Step-by-step explanation:

What is the measure of angle r

Answers

Answer:

Step-by-step explanation:

you have a pentagon , and the sum of the angles is 540

3x-10+3x-8+5x-2+3x+1+2x+15=16x-4=540

16x-4=540

16x=544

x=544/16=34

the angle= (3x-8)=(3*34)-8=94


Help me pls it’s due today at 11:59

Answers

Answer:

A rotation followed by a translation

need help with this

Answers

Answer:

y = 1

Step-by-step explanation:

Since 15 and 5, 18 and 6, and 27 and 9 all have 3 in common, then 3 should go into 1.

Answer:

1

Step-by-step explanation:

equation is always x/3=y

Sam knows that there are 12 inches in 1 foot. He has a string that is 3 1/2 feet long. What is the length of the string , in inches?

Answers

Answer:

42 in

Step-by-step explanation:

12 x 3 = 36

1/2 foot = 6 in

36 + 6 = 42

Someone please help!

Answers

Answer:

3.25

Step-by-step explanation:

it is shrinking by a factor of 4 so every number is 4 times smaller and 13 divided by 4 will give you 3.25

Answer:

3.25

Step-by-step explanation:

As you can see from the one on the left and the other on the right is that the left is larger than the right by the ratio of 4:1

CB = 12, ZY = 3

BA = 5, YX = 1.25

Using this information, to find ZX, we just need to divide CA's  length by 4:

13 / 4 = 3.25

please answer thank you

Answers

Answer:

8.1 for the 2th awnser

Step-by-step explanation:

1.4 + 5.9+2.2=8.1

Answer:

z (3.4 + 4.6 + 2.2)

:)

In order to help me move, I got a credit card with a $1,000 credit limit and spent all $1,000 the first month. The credit card charges compound interest at a rate of 15% a month, BUT, you don’t have to make any payments for one year. How much debt will I have after 1 year of having this card?

Answers

Answer

The tax/ your paying a year is 150, so you would owe 1,500 btw, answer my recent question maybe..?

Step-by-step explanation:

Steps for solving multi-step equations:

Simplify by ____________________ like terms or _______________________

(there should only be one variable after this step)

Undo any _________________ or _________________ 3. Undo any ________________ or __________________

4. _______________ answer.

Answers

Answer:

What are two-step equations?

A two-step equation is an algebraic equation you can solve in two steps. Once you've solved it, you've found the value of the variable that makes the equation true.

Example 1

We're given an equation and asked to solve for

x

xx:

3

x

+

2

=

14

3x+2=143, x, plus, 2, equals, 14

We need to manipulate the equation to get

x

xx by itself.

3

x

+

2

=

14

3

x

+

2

2

=

14

2

3

x

=

12

3

x

3

=

12

3

x

=

4

3x+2

3x+2−2

3x

3

3x

x

=14

=14−2

=12

=

3

12

=4

The solution:

x

=

4

x=4start color #1fab54, x, equals, 4, end color #1fab54

It's always a good idea to check our solution in the original e

3

x

+

2

=

14

3

4

+

2

14

12

+

2

14

14

=

14

Yes!

3x+2

3⋅4+2

12+2

14

=14

=

?

14

=

?

14

=14 Yes!

Want to learn more about two-step equations? Check out this video.

Example 2

We're asked to solve this equation for

a

aa:

8

=

a

3

+

6

8=

3

a

+68, equals, start fraction, a, divided by, 3, end fraction, plus, 6

We need to manipulate the equation to get

a

aa by itself.

8

=

a

3

Can somebody help please?

Answers

Answer:

Answer is D

Step-by-step explanation:

Answer:uh i think D

Step-by-step explanation:

Need help (8th grade math)

Answers

Slope= rise/run

=y2-y1/x2-x1

3-1/8-7

2/1

Slope=2

Answer:

2

Step-by-step explanation:

- use the equation:

m=y^2-y^1/x^2-x^1

- pick any two points:

m= -1+3/6-5

- solve:

m= 2/1

FINAL ANSWER:

2

What is 2.419 rounded to the nearest one?

Answers

Answer:

2

Step-by-step explanation:

5 jakxoxodmenkxnwmzx

I will mark brainliest please help ​

Answers

Answer:

15 cups

Step-by-step explanation:

The formula to find cups from quarts C = Q * 4, where c is how many cups, and Q how many quarts. To find how many cups are in a quart, simply multiply the number of quarts by 5. In this case, there are 3 3/4 quarts of coffee, multiply that by 5, and you would get 15 cups of coffee!

Question 1 (5 points)
The height of a kicked football can be represented by the polynomial -16+47t+3
= 0, where tis the time in seconds. Find the time in seconds of when the football hits
the ground.
A) 3 seconds
B) 2.5 seconds
C) 1 second
D) O seconds

Answers

Answer:

A. 3 secseconds

Move 16 and 3 to the other side and divide

4.012+ S equals 5.313

Answers

Answer:

S= 1.301

Step-by-step explanation:

5.313-4.012=S

the answer is
S=1.301
This is because
4.012+1.301=5.313
Hope this helps have a good day! ;)

Nike shoes are 45% off $80.
What will be the savings
on
the
tennis shoes ?

Answers

You will pay $44 for the shoes

Answer:

You pay  $44 / You're saving $36

Step-by-step explanation:

100 - 45 = 55

$80 x 0.55 = $44

?????????????????????

Answers

White her is white b

Answer:

f(9) = 61

Step-by-step explanation:

You know f(x) = 8x - 11. So, to find f(9), you have to replace x with 9 on the other side.

f(9) = 8(9) - 11

You can solve this.

f(9) = 72 - 11

f(9) = 61

help please and u get a cookie

Answers

Answer:

im allergic to cookies

Step-by-step explanation:

Item 4: Help! asapnplease

Answers

Answer:

The answer tot he question provided is 5.

Step-by-step explanation:

→ Angle D and Angle B are congruent to each other, which means that they are equal.

→ The equation would look like:

[tex]2x + 4 = 4x - 6[/tex]

→ Solve the equation.

[tex]2x + 4 = 4x - 6 \\ \frac{ - 4x \: \: \: \: = - 4x \: \: \: \: \: \: \: \: \: }{ - 2x + 4 = - 6} \\ \frac{ \: \: \: \: \: \: \: \: \: \: \: - 4 = - 4}{ \frac{ - 2x}{ - 2} = \frac{ - 10}{ - 2} } \\ x = 5[/tex]

→ The value of x results in being 5.

Round 992 to the nearest ten

Answers

It will be 990 hope this helps

Answer:

990

Step-by-step explanation:

990

2 is lower than 5 so we round down. Instead of rounding up to 1, round down to 0

In a NFL game in December the Seattle Seahawks scored 16 of their 40 points in the second quarter. What percent of their total points were made in the second quarter?

Answers

Answer:

That would be 40%.

On Thursday, 14 out of 20 cookies sold at a bakery were Chocolate Chip. What percent of the cookies sold at the bakery were Chocolate chip?

Answers

14/20=0.7
70% of the cookies were Chocolate chip
:)

What is the opposite of -5?

Answers

Step-by-step explanation:

the opposite of -5 is +5

have a great dayyyy :)

It’s +5 or the normal Whole number 5

Enter the area of a square with a diagonal of 18 feet. Round to the nearest whole number. Just the number, no units please. We know it is feet squared. *

Answers

Answer: 162

Explanation:

The formula is 1/2d^2

1/2 = 0.5 18^2 = 324 324 x 0.5 = 162

Solve for x round to one decimal place.

Answers

Answer:

i wanna say 12 but i am not sure!!!!!!!!!

Step-by-step explanation:

A square pyramid is shown below:

A square pyramid is shown. The sides of the square base are labeled 0.7 foot. The height of one of the triangular sides is labeled 8 feet.
What is the surface area of the pyramid? (1 point)

11.69 square feet
3.29 square feet
7.49 square feet
2.24 square feet

Answers

Answer: A 11.69

Step-by-step explanation:

Answer:

11.69

Step-by-step explanation:

i need pts

Divide and find answer

Answers

Answer:

Step-by-step explanation:

11 is A ( i think)

12 i know is c but if wrong im so sorry

hope this helps

A bowl of soup at 95!C (too hot) is placed in a 22!C room. One minute later, the soup has cooled to 83!C. When will the temperature be 49!C (just right)?

Answers

Answer:

in 3 minutes and 50 seconds

Step-by-step explanation:

soup = 95c

after 1 minute = 83c

after 2 minutes = 71c

after 3 minutes = 59

soup cools down 0.2c in 1 seconds

so 10 seconds = 2c

in 3 minutes and 50 seconds = 49c

The temperature 49°C of soup bowl will be after 5.54 minutes

Newton law of coolingAccording to Newton's law of cooling, the rate of loss of heat from a body is directly proportional to the difference in the temperature of the body and its surroundingsThe formula is as follow:

[tex](T-T_{s} )=(T_{0} -T_{s} )e^{-kt}[/tex]

What are the steps to solve this problem?Given

[tex]T =[/tex] 83°C and 49°C

[tex]T_{s} =[/tex] 22°C

[tex]T_{0} =[/tex] 95°C

We have to find value of t for that first we will find value of k and applying all values in formula we get,

(83-22)=(95-22)[tex]e^{-k}[/tex]

∴ k = -ln (61/73)

Now,

(49-22) = [tex]e^{ln(61/73)t}[/tex]

∴ t = [tex]\frac{ln (27/73)}{ln(61/73)}[/tex]

∴ t = 5.54 minutes

So, after 5.54 minutes temperature will be 49°C

Learn more about Newton's Law of Cooling here:

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PLEASE HELP ME,I’ve been trying all morning
If f(x)= x^2 + 2x + 5, what is f(x + 3)?

Answers

Answer:

Step-by-step explanation:

f(x) = x² + 2x + 5

f(x+3) = (x+3)² + 2(x+3) + 5

  = (x²+6x+9) + (2x+6) + 5

  = x² + 8x + 20

Answer:

you sure its not f(x+3) ?

Step-by-step explanation:

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