While passing a slower car on the highway, i accelerate uniformly from 12 m/s to 24 m/s in a time of 10.0s. How far do you travel during this time and what is the magnitude of your acceleration

Answers

Answer 1

You say that there is uniform acceleration so:

vf-vi=at (final velocity minus initial velocity is equal to acceleration times time)

We know vf, vi, and t so we can solve for acceleration:

24-12=a10

12=10a

a=1.2

That is the acceleration, we will need to integrate with respect to time twice...

v=⌠a dt

v=at+vi , we know a=1.2m/s^2 and vi=12m/s

v=1.2t+12,

x=⌠1.2t+12 dt

x=1.2t^2/2+12t+xo, we can just let xo=0 for this problem...

x(t)=0.6t^2+12t

Now we know that this acceleration lasts for 10 seconds so the distance traveled in that time is:

x(10)=0.6(10^2)+12(10)

x(10)=60+120

x(10)=180 meters

Related Questions

Kathy walked 3 1/2 miles per hour for 1 1/4 hours. During 1/2 of her walking time it rained. How many miles did she walk while it was raining?

Answers

I think it's 2.2 miles walking in the rain

1 1/4 = 5/4 * 1/2 = 5/8

3 1/2 = 7/2 * 5/8 = 35/16 = 2 3/16 miles

Atmospheric pressure decreases by about 11.8% for every 1000 meters you climb. The pressure at sea level is 1013 millibars (a unit of pressure). Construct an exponential model to represent the atmospheric pressure at a given altitude in thousands of meters. Use your model to determine the atmospheric pressure at an altitude of 4000 meters.
(Express your answer in millibars rounded correctly to the nearest tenth.)

Answers

at sea level, the pressure is 1013, that's when the altitude is at 0, sea level, let's see

[tex]\bf \textit{Periodic Exponential Decay}\\\\ A=I(1 - r)^{\frac{t}{p}}\qquad \begin{cases} A=\textit{accumulated amount}\to &1013\\ I=\textit{initial amount}\\ r=rate\to 11.8\%\to \frac{11.8}{100}\to &0.118\\ t=\textit{meters climbed}\to &0\\ p=period\to &1000 \end{cases} \\\\\\ 1013=I(1-0.118)^{\frac{0}{1000}}\implies 1013=I\cdot 1\implies 1013=I[/tex]

so, the inital amount is 1013, when t = 0,

[tex]\bf \textit{Periodic Exponential Decay}\\\\ A=I(1- r)^{\frac{t}{p}}\qquad \begin{cases} A=\textit{accumulated amount}\\ I=\textit{initial amount}\to &1013\\ r=rate\to 11.8\%\to \frac{11.8}{100}\to &0.118\\ t=\textit{meters climbed}\to &t\\ p=period\to &1000 \end{cases} \\\\\\ A=1013(1-0.118)^{\frac{t}{1000}}\implies A=1013(0.882)^{\frac{t}{1000}}[/tex]

now, to check the atmospheric pressure at 4000, simply set t = 4000, to get A.

What statement regarding the diagram is true?

Answers

I believe the second one right, because if I remember two opposite angles of an outside angle = the outside angle.

The volume of the Moon is about 2.18×10102 cubic kilometers. The volume of Earth is about 1.09×10121 cubic kilometers. The number of Moons that can fit inside Earth can be found by dividing Earth's volume by the Moon's volume. About how many Moons can fit inside Earth?

Answers

Volume of Earth is 1.09×1012 cubic kilometers

Volume of Moon is 2.18×1010 cubic kilometers

Hence number of Moons that can fit in Earth is

1.09×10122.18×1010

= 1012−102 as 2.18=1.09×2

= 1022

= 1002=50

Answer:

50 moons

Step-by-step explanation:

cause i got it right on the test

how many miles can you drive with 13.2 gallons of gasoline

Answers

286.44 I multiplied the numbers together

This depends on how large your car is and how fast you drive.
Certain cars burn more gasoline than others. You also may burn more or less gasoline depending on your speed. Slower speeds burn less, whereas faster speeds burn more.

Out of 30 students surveyed 17 have a dog based on these results predict how many of the 300 students in the school have a dog

Answers

17/30 = 0.5666 so about 57% of the sample had dogs

300 x 0.57 = 171 would have dogs

The extreme rock climbing club planned a climbing expedition. The total cost was $5000, which was to be divided equally among the members going. Prior to the trip, 3 members decided not to go. If the cost per person increases by $375, how many people went on the expedition?

Answers

Most useful original number of planned climbers were 687 members .hope i helped

687 I am pretty sure hope it helps,,,,,,,,,,m,,,,

What property describes the number sentence? 6+0=6

Answers

hello :
the property describes the number sentence 6+0=6 is : " 0 Neutral element for addtion"

The perimeter of a rectangular field is 168 feet. The field is 36 feet wide. How long is the field

Answers

To find the length, divide the peremiter by 2 and then subtract the width.

Length= Peremiter/2 - width
L = P/2 - W
L = 168/2 - 36
L = 84 - 36
L = 48

The length is 48

A wheelchair access ramp has an angle of elevation of 20°. If the ramp reaches to the top of a 33 inch high porch, how long is the ramp?

Answers

sinα=height/length

length=height/sinα, we are given that α=20° and h=33 in

length=33/sin20° in

length≈96.49 in (to nearest hundredth of an inch)

This is a sin operation, Sin is the relationship between the opposite (height) and the hypotenuse (length of ramp). Plugging in: Sin(20deg) = 33/x

Sin(20) = 33/x

x*Sin(20) = 33

x = 33/Sin(20)

x = 96.49in long.

*This answer is the length of the SLOPE of the ramp.

If a wheel with a radius of 80 inches spins at a rate of 50 revolutions per minute, find the approximate linear velocity in miles per hour.

Answers

[tex]\bf \textit{arc's length}\\\\ s=rw\qquad \begin{cases} r=radius\\ w=\textit{angular speed} \end{cases}\qquad w=\cfrac{50 rev}{min}\cdot \cfrac{2\pi }{rev} \\\\\\ w=\cfrac{100\pi }{min}\qquad s=80in\cdot \cfrac{100\pi }{min}\implies s=\cfrac{8000\pi\ in}{min}\\\\ -------------------------------\\\\ \textit{now to convert it to miles/hr} \\\\\\ \cfrac{8000\pi\ in}{min}\cdot \cfrac{ft}{12in}\cdot \cfrac{mile}{5280ft}\cdot \cfrac{60min}{hr}\implies \cfrac{8000\pi \cdot 60\ in}{12\cdot 5280\ hr}[/tex]

Find a_1 and d for an arithmetic sequence with these terms. a_4=9and a_7=18

Answers

[tex]\bf \begin{array}{llll} term&value\\ -----&-----\\ a_4&9\\ a_5&9+d\\ a_6&(9+d)+d\\ &9+2d\\ a_7&(9+2d)+d\\ &9+3d=\underline{18} \end{array}\\\\ -------------------------------\\\\ 9+3d=18\implies 3d=9\implies d=\cfrac{9}{3}\implies \boxed{d=3}[/tex]

[tex]\bf n^{th}\textit{ term of an arithmetic sequence}\\\\ a_n=a_1+(n-1)d\qquad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ d=\textit{common difference}\\ ----------\\ n=7\\ d=3 \end{cases} \\\\\\ a_7=a_1+(7-1)d\implies 18=a_1+(7-1)3\implies 18=a_1+18 \\\\\\ 18-18=a_1\implies \boxed{0=a_1}[/tex]

You deposit $5000 in an account earning 2% interest compounded continuously. How much will you have in the account in 15 years?

Answers

The compound interest is given by:
A=p(1+r/100)^n
where:
A=future amount
p=principle
r=rate
n=time in years
Therefore given that, p=$5000, r=2% and n=15 years, the amount after 15 years will be:
A=5000(1+2/100)^15
A=5000(1+0.02)^15
A=5000(1.02)^15
A=6,729.34
We conclude that the amount after 15 years will be $6,729.34

You are trying to determine the half-life of a new radioactive element you have isolated. You start with 1 gram, and 5 days later you determine that it has decayed down to 0.7 grams. What is its half-life? (Round your answer to three significant digits.)

Answers

The half-life of a given radio active material is given by:
t(1/2)=[tln2]/[lnN-lnN(t)]
where;
t=time
N=initial amount
N(t)=final amount
thus the half-life of our material will be as follows:
t=5 days
N=1 g
N(t)=0.7 g
N(1/2)=[5*ln2]/[ln1-ln0.7]
=9.717

A rug is shaped like a rectangle who's per Perimeter there's 192 feet the length is five times longer with find the length and the width

Answers

P = Perimeter = 2(length) + 2(width). Let the width be x; then if the length is 5 times longer than the width, the length is 5x.

Plug these values into the Perimeter equation P = 2(length) + 2(width):

P = 2(5x) + 2(x), or P = 12x, and this is known to have the value 192 units. Solve for the width, x:

(192 units) = 12x gives us x = 16 units. Then the length is 5(16 units) = 80 units.

Check: Does 2(80 units) + 2(16 units) = 192 units? If so, then our width (16) and length (80) are correct.

Evaluate the limit using the appropriate limit law(s). (if an answer does not exist, enter dne.) lim x → 1 2x2 + 4 x2 + 4x − 4

Answers

Presumably, the limit to be evaluated is

[tex]\displaystyle\lim_{x\to1}\frac{2x^2+4}{x^2+4x-4}[/tex]

Since the given function is continuous at [tex]x=1[/tex], the limit of function is equal to the value of the function at [tex]x=1[/tex]:

[tex]\displaystyle\lim_{x\to1}\underbrace{\frac{2x^2+4}{x^2+4x-4}}_{f(x)}=f(1)=\frac{2+4}{1+4-4}=6[/tex]

a triangular prism has height of 10cm and a base area of 12cm. a rectangular prism has height of 10cm and base dimensions of 3 cm and 4 cm. do the solids have the same volume?

Answers

check the picture below.

notice, the base area of the rectangular prism is just 3x4.

What's the answer to the equation;
√2y+3=11

Answers

y=59 that should be the correct answer

The answer should be Y=32 should be it

what is the remainder when 3 is synthetically divided into the polynomial -x^2+5x-9

Answers

-3 is the remainder when you synthetically divide

Answer:

REmainder is -3

Step-by-step explanation:

find remainder when 3 is synthetically divided into the polynomial -x^2+5x-9

In synthetic division we write all the coefficient of the polynomial and divide by 3

3 -1 5 -9

0 -3 6

-------------------------------

-1 2 -3 ----> Remainder

So the remainder is -3

Which of the following gives all of the sets that contain -1/2?

A.the set of all rational numbers and the set of all real numbers
B.the set of all natural numbers and the set of all irrational numbers
C.the set of all integers and the set of rational numbers
D.the set of all natural numbers, the set of rational numbers, and the set of all real numbers

Answers

i think it might be.... A.the set of all rational numbers and the set of all real numbers

Answer:

Option A is Correct Option.

Step-by-step explanation:

Given: [tex]\frac{-1}{2}[/tex]

[tex]\frac{-1}{2}[/tex] is a rational no.

Option A:

Given no is a rational no.

⇒ Both Set of rational no and real nos. contain rational nos..

Thus, Correct Option.

Option B:

set of natural nos and irrational nos does not contain rational nos.

Thus, Not correct option.

Option C:

Set of integers does not contain rational numbers.

Thus, Incorrect Option.

Option D:

Set of all Natural Nos. does not contain rational nos.

Thus, This option is not correct option

Therefore, Option A is Correct Option.

The table below represents the distance of a train from its destination as a function of time: Time (hours) x Distance (miles) y 0 665 1 570 2 475 3 380 4 285 Part A: What is the y-intercept of the function, and what does this tell you about the train? (4 points) Part B: Calculate the average rate of change of the function represented by the table between x = 1 to x = 4 hours, and tell what the average rate represents. (4 points) Part C: What would be the domain of the function if the train continued to travel at this rate until it reached its destination? (2 points)

Answers

A. y=-95x+665 y-intercept is 665
B. Ave rate of change is -95
C. y=0 so x=7 Domain is [0,7]

The axis of symmetry for a quadratic equation can be found using the formula x =-b/2a , where a and b are coefficients in the quadratic equation and x represents the values along a vertical line on the coordinate plane. When the equation is solved for a, such that b is the numerator of the resulting fraction, what is the denominator of the fraction?

2x

–2x

1/2x

–1/2x

Answers

if x = -b/2a, then 2a = -b / x so a = -b / 2x or a = b / -2x

So the denominator is -2x because it has to take the minus sign that the numerator refused to take ;-)

The answer is B on edgen.

What is the height of a cylinder with a volume of 315 pi cubic meters and a radius of 6 meters? 8.75 meters 12.25 meters 26.25 meters 52.5 meters

Answers

check the picture below.

simplify away.

Since this cylinder has a radius of 6 meters, its height is equal to 8.75 meters.

Given the following data:

Radius of cylinder = 6 m.

Volume of cylinder = 315π m.

How to calculate the height of this cylinder?

Mathematically, the volume of a cylinder is calculated by using this formula:

V = πr²h

Where:

h is the height.r is the radius.

Substituting the given parameters into the formula, we have;

315π = π × 6² × h

315π = 36πh

h = 315/36

Height, h = 8.75 meters.

Read more on cylinder here: brainly.com/question/21367171

#SPJ2

The length of a shadow of a building is
29 m
. The distance from the top of the building to the tip of the shadow is
35 m
. Find the height of the building

Answers

h^2=x^2+y^2

35^2=29^2+y^2

y^2=35^2-29^2

y^2=384

y=√384

y≈19.60 m (to the nearest hundredth of a meter, or nearest centimeter)

The course for a walkathon is 6 miles long. If Chloe wants to walk 50 miles during the walkathon, how many times must she walk the course?

Answers

she should walk the course about 8 or 9 times

divide 50 by 6

50/6 = 8.333

so she has to walk it 8.33 times

round answer as needed.

Keeping in mind that a functions rate of change is measure of how fast the function is increasing or decreasing what does the slope of a linear function indicate?

Answers

When a linear function is graphed, a line will drawn on the plot. If we analyze this, this means that the two variables are related by a constant of proportionality. That constant is called the slope. Since the slope is constant, that means that the rate of change is also constant. It would only differ if the rate is increasing or decreasing. It would be increasing if its magnitude is positive which will be graphed as a diagonal to the right. Otherwise, it is decreasing whose magnitude is negative which will be graphed as a diagonal to the left.

Answer: A linear function is represented as a straight line. The slope of the line gives the function’s rate of change.

Step-by-step explanation: Plato sample answer

Matthew currently has enough money to buy 45 toy cars. If the cost of each car was 10 cents less, Matthew could buy 5 more cars. How much money does Matthew have to spend on toy cars?

Answers

x=price per toy car
45x = money Matt has
45x =50(x-.1)
45x =50x -5
5 =5x
x=$1
45x= $45
the cost of each car is $1

The total ages of 2 buildings is 201 years. if one building is twice as old as the other, what are the ages of 2 buildings?

Answers

Answer: 67 years and 134 years

In this case, you are given the buildings sum ages ( building A ages+ building B ages = 201 years) and the building ratio ( Building A ages= 2x Building B ages).
To answer the question, you simply need to insert the second equation into the first. It would be:

building A ages + building B ages= 201
2x building B ages + building B ages= 201
building B ages= 67 years.

Then building A ages= 2x 67 years= 134 years.

The ages of the two buildings are 67 and 134 years. This is found by setting up an algebraic equation where the sum of their ages is 201, and one is twice as old as the other.

Finding the Ages of Two Buildings

If the total ages of two buildings is 201 years and one building is twice as old as the other, then we can express the ages of the buildings using algebra. Let's denote the age of the younger building as y years. The older building is twice as old, so its age would be 2y years. The equation based on their total ages would be:

y + 2y = 201 years

Solving this equation:

Combine like terms: 3y = 201.

Divide both sides by 3 to isolate y: y = 201 / 3.

Calculate the exact value: y = 67 years.

So, the younger building is 67 years old, and the older building, being twice as old, is 134 years old.

A math teacher gave her class two tests. 76% of the class passed the first test. 58% of the class passed both tests. What is the approximate probability that a student who passed the second test, given that he passed the first test.

Answers

P(test 2 | test 1) = P(test 2∩test 1) ÷ P(test 1)
P(test 2 | test 1) = 0.58 ÷ 0.76
P(test 2 | test 1) = 0.76 ≈ rounded to two decimal places

Suppose an isosceles triangle ABC has A = 45° and b = c = 4. What is the length of a2?

Answers

You can use the Law of Cosines (a^2=b^2+c^2-2bc cosA)

a^2=4^2+4^2-2*4*4*cos45°

a^2=32-32cos45°

a^2=32(1-cos45°)

a=√(32(1-cos45°))

a≈3.06 units (to nearest hundredth of a unit)

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