PLEASE HELP
Section 1 - Question 6
Wave Movement Through Media
What could be happening to the wave as it travels from left to right?
A
It's moving through a medium whose density stays the same
B
It's moving from a low density medium to a high density medium.
С
It's moving from a high density medium to a low density medium.
D
It's moving from a low density medium, to a high density medium, and then back to a low density medium

PLEASE HELP Section 1 - Question 6Wave Movement Through MediaWhat Could Be Happening To The Wave As It

Answers

Answer 1

Answer: B

Explanation:


Related Questions

a boy throws a ball straight up into the air it reaches the highest point of its flight after 4 seconds how fast was the ball going when it left the boy's hand

Answers

Answer:

Gravity pulls down on the ball at g=-9.81 m/s^2. Up is positive, down is negative. The ball started at a certain initial velocity of Vi m/s. Time it took is t=4s. Final velocity is Vf=0 m/s, because at the highest point the ball stops moving.

A potter's wheel is rotating around a vertical axis through its center at a frequency of 2.0 rev/srev/s . The wheel can be considered a uniform disk of mass 4.5 kgkg and diameter 0.30 mm . The potter then throws a 2.8-kgkg chunk of clay, approximately shaped as a flat disk of radius 8.0 cmcm , onto the center of the rotating wheel. Part A What is the frequency of the wheel after the clay sticks to it

Answers

Answer:1.7 rev/s

Explanation:

Given

Frequency of wheel [tex]N_1=2\ rev/s[/tex]

angular speed [tex]\omega_1=2\pi N_1=4\pi\ rad/s[/tex]

mass of wheel [tex]m_1=4.5\ kg[/tex]

diameter of wheel [tex]d_1=0.30\ m=30\ cm[/tex]

radius of wheel [tex]r_1=\frac{d_1}{2}=\frac{30}{2}=15\ cm[/tex]

mass of clay [tex]m_2=2.8\ kg[/tex]

the radius of the chunk of clay [tex]r_2=8\ cm[/tex]

Moment of inertia of Wheel

[tex]I_1=\dfrac{m_1r_1^2}{2}=\dfrac{4.5\times 15^2}{2}\ kg-cm^2[/tex]

Combined moment of inertia of wheel and clay chunk

[tex]I_2=\dfrac{m_1r_1^2}{2}+\dfrac{m_2r_2^2}{2}=\dfrac{4.5\times 15^2}{2}+\dfrac{2.8\times 8^2}{2}\ kg-cm^2[/tex]

Conserving angular momentum

[tex]\Rightarrow I_1\omega_1=I_2\omega_2\\\Rightarrow \dfrac{4.5\times 15^2}{2}\cdot 4\pi=(\dfrac{4.5\times 15^2}{2}+\dfrac{2.8\times 8^2}{2})\omega_2\\\\\Rightarrow \omega _2=\dfrac{4\pi }{1+\dfrac{2.8}{4.5}\times (\dfrac{8}{15})^2}=\dfrac{4\pi}{1+0.1769}=0.849\times 4\pi[/tex]

Common frequency of wheel and chunk of clay is

[tex]\Rightarrow N_2=\dfrac{4\pi \times 0.849}{2\pi}=1.698\approx 1.7\ rev/s[/tex]

Investigator Daniels is working on the scene of a suspected arson on a rainy evening. The site of the fire was a mechanic's garage, so there are plenty of accelerants
on the scene. According to the owner of the garage, there had been an argument with a customer the day before about his motorcycle. All the employees left by
6:00 pm. The office was unharmed but there is much damage in the mechanic's bay area and toolboxes. The flames look to have been most concentrated around a
bucket that the owner says was filled with oily rags. She is trying to sift through the evidence and find the relevant facts of the case so far. In order to effectively
Identify the relevant facts, Investigator Daniels creates a word bank. Which word would not fit into her word bank?
Argument
Rainy
Olly rags
Toolboxes

Answers

Answer:

Rainy

Explanation:

It is the only one that has nothing to do with the case

If soldiers march across the bridge with a cadence equal to the bridge’s natural frequency and impart 1x104 J of energy each second, how long does it take for the bridge’s oscillations to go from 0.1 m to 0.5 m amplitude?

Answers

Answer: Hello, Mark me as Brainliest! :)

If soldiers march across the bridge with a cadence equal to the bridge's natural frequency and impart $$1.00 × 10^4 J$$ of energy each second, how long does it take for the bridge's oscillations to go from 0.100 m to 0.500 m amplitude. $ 5 \times 10^7 \text{J} $ . \\ b) $ 12 \times 10^4 \text{s}$ .

Your Welcome!

Explanation:

What is the scientific study of how animals are classified?

Answers

Answer:

biology

Explanation:

Animals and plants

what colors of light are absorbed when white light falls on a green object?

Answers

It’s blue because it makes it go in to it and sink

Solve the below problems being sure to provide the correct significant figures.

1) 1000 ÷ 4.886 = __________

2) 240 ÷ 12.3 = __________

3) 80 x 4.6 = __________

4) 4.527 x 30 = __________

5) 86 x 63.855 x 8000 = __________

6) 700 x 91.186 = __________

7) 7.1 x 348 = __________

8) 50 ÷ 29.1 = __________

9) 98.773 x 24.891 x 409 = __________

10) 0.065 x 3 x 3007 = __________

Answers

Answer:

1) 204.6663938

2) 19.51219512

3) 368

4) 135.81

5) 43932240

6) 63830.2

7) 2470.8

8) 1.718213058

9) 1005550.526

10) 586.365

Most of the questions you asked were in repeating decimal form.

Explanation:

If we always drop the balls from 1-m
height in each trial, what type of variable
is this in this experiment?
Constant Variable
Dependent Variable
Independent Variable

Answers

Answer:

height

weight of ball

time of ball falling

Two resistors have resistances R1 and R2. When the resistors are connected in series to a 12.6-V battery, the current from the battery is 2.07 A. When the resistors are connected in parallel to the battery, the total current from the battery is 8.98 A. Determine R1 and R2. (Enter your answers from smallest to largest.)

Answers

Answer:

When R1 = 2.193, R2 = 3.894

When R1 = 3.894, R2 = 2.193

Explanation:

We are told that when R1 and R2 are connected in series, the voltage is 12.6 V and the current is 2.07 A.

Formula for resistance is;

R = V/I

R = 12.6/2.07

R = 6.087 ohms

Since R1 and R2 are connected in series.

Thus; R1 + R2 = 6.087 ohms

R1 = 6.087 - R2

We are also told that when they are connected in parallel, the current is 8.98 A.

Thus, R = 12/8.98

R = 1.403 ohms

Thus;

(1/R1) + (1/R2) = 1/1.403

Let's put 6.087 - R2 for R1;

(1/(6.087 - R2)) + (1/R2) = 1/1.403

Multiply through by 1.403R2(6.087 - R2) to get;

1.403R2 + 1.403(6.087 - R2) = R2(6.087 - R2)

Expanding gives;

1.403R2 + 8.54 - 1.403R2 = 6.087R2 - (R2)²

(R2)² - 6.087R2 + 8.54 = 0

Using quadratic formula, we have;

R2 = 2.193 ohms or 3.894 ohms

Thus,

R1 = 6.087 - 2.193 or R1 = 6.087 - 3.894

R1 = 3.894 or 2.193

When R1 = 2.193, R2 = 3.894

When R1 = 3.894, R2 = 2.193

Which of the following have frequencies greater than orange light Your answer:
radio waves
purple light
ultraviolet rays
red light
green light
gamma rays
microwaves
infrared rays

Answers

Answer:

Gamma Rays have the highest frequencies

Explanation:

This is because Gamma rays have the highest energies, the shortest wavelengths, and the highest frequencies compared to the other light frequency. Radio waves, on the other hand, have the lowest energies, longest wavelengths, and lowest frequencies of any type of EM radiation which means the answer has to be gamma rays. Brainly Please!!!! Here are screenshots that may help

Mechanical energy is the most concentrated form of energy.
a. true
b. false

Answers

( False )Nuclear energy is the most concentrated form of energy.

As a delivery truck travels along a level stretch of road with constant speed, most of the power developed by the engine is used to compensate for the energy transformations due to friction forces exerted on the delivery truck by the air and the road. If the power developed by the engine is 4.12 hp, calculate the total friction force acting on the delivery truck (in N) when it is moving at a speed of 30 m/s. One horsepower equals 746 W.

Answers

Answer:

102.5N

Explanation:

Given that  a delivery truck travels along a level stretch of road with constant speed, most of the power developed by the engine is used to compensate for the energy transformations due to friction forces exerted on the delivery truck by the air and the road. If the power developed by the engine is 4.12 hp, calculate the total friction force acting on the delivery truck (in N) when it is moving at a speed of 30 m/s. One horsepower equals 746 W

The power = 4.12 × 746 = 3073.52 W

Using the formula

Power = force × velocity

3073.52 = force × 30

Force = 3073.52 / 30

Force = 102.5 N

Since most of the power developed by the engine is used to compensate for the energy transformations due to friction forces exerted on the delivery truck by the air and the road, therefore,

the total friction force acting on the delivery truck (in N) when it is moving at a speed of 30 m/s is 102.5 N

NEED HELP ASAP, ILL GIVE YOU BRAINLIEST IF CORRECT (30POINTS)


Drag each label to the correct location on the image. Each label can be used more than once.

Identify the parts of the barred spiral galaxy.

SPIRAL ARM, NUCLEUS, BAR


NOTE I JUST FILLED IN THE SPOTS FOR YOU TO SEE, THEY ARE NOT CORRECT

Answers

Answer:

the bar is the top and bottem. the nucleas in the middle and the Spiral arm is the last space

Explanation:

Answer:

look pkch

Explanation:

When6-2 He He-6 undergoes beta decay, the daughter is?​

Answers

Answer: The daughter is named Susie.

Explanation: LIL SUSIE!!!

                      HUH? DIDN'T UNDERSTAND THE QUESTION!

                                        HAVE A GREAT DAY!!!!!

Answer:6/3 Li

Explanation:

I’m not sure what the person under me is talking about but yeah

I don’t understand this

Answers

What was the question? I can help I just need the question !

Answer:

true

Explanation:

force or powerbecause he pushes a disk

Force exerted on a body changes it's

Answers

Momentum is the answer

an iron Tyre of diameter 50cm at 288k is to be shrank on to a wheel of diameter 50.35cm.To what temperature must the tyre be heated so that it will slip over the wheel with a radial gap of 0.5mm.Linear expansivity of iron is 0.000012k-1

Answers

Answer:

The answer should be D

Explanation:

The amount of light that enters the pupil is controlled by the:
retina.
lens.
inis.

Answers

Answer: The amount of light that enters the pupil is controlled by the Iris

Explanation:

Two 10-cm-diameter charged rings face each other, 21.0 cm apart. Both rings are charged to +40.0 nC. What is the electric field strength ?

Answers

Complete question:

Two 10-cm-diameter charged rings face each other, 21.0 cm apart. Both rings are charged to +40.0 nC. What is the electric field strength  at the midpoint between the two rings ?

Answer:

The electric field strength at the mid-point between the two rings is zero.

Explanation:

Given;

diameter of each ring, d = 10 cm = 0.1 m

distance between the rings, r = 21.0 cm = 0.21 m

charge of each ring, q = 40 nC = 40 x 10⁻⁹ C

let the midpoint between the two rings = x

The electric field strength  at the midpoint between the two rings is given as;

[tex]E_{mid} = E_{right} +E_{left}\\\\E_{right} = \frac{KQ}{(x^2 + r^2)^\frac{2}{3} } \\\\E_{leftt} = -\ \frac{KQ}{(x^2 + r^2)^\frac{2}{3} }\\\\E_{mid} = \frac{KQ}{(x^2 + r^2)^\frac{2}{3} } - \frac{KQ}{(x^2 + r^2)^\frac{2}{3} } = 0[/tex]

Therefore, the electric field strength at the mid-point between the two rings is zero.

A bump should primarily be used in which situation?

A. when the ball is going out of bounds
B. when returning a serve
C. to start game play

Answers

The answer is b to the question

Calculate the first and second order angles for light of wavelength 400. nm and 700. nm of the grating contains 1.00 x 104 lines/cm.

Answers

Answer:

[tex]23.58^{\circ}[/tex] and [tex]53.13^{\circ}[/tex]

[tex]44.43^{\circ}[/tex], second order does not exist

Explanation:

n = Number of lines grating = [tex]1\times10^4\ \text{Lines/cm}[/tex]

[tex]\lambda[/tex] = Wavelength

m = Order

Distance between slits is given by

[tex]d=\dfrac{1}{n}\\\Rightarrow d=\dfrac{1}{1\times 10^4}\\\Rightarrow d=10^{-6}\ \text{m}[/tex]

[tex]\lambda=400\ \text{nm}[/tex]

m = 1

We have the relation

[tex]d\sin\theta=m\lambda\\\Rightarrow \theta=\sin^{-1}\dfrac{m\lambda}{d}\\\Rightarrow \theta=\sin^{-1}\dfrac{1\times 400\times 10^{-9}}{10^{-6}}\\\Rightarrow \theta=23.58^{\circ}[/tex]

m = 2

[tex]\theta=\sin^{-1}\dfrac{2\times 400\times 10^{-9}}{10^{-6}}\\\Rightarrow \theta=53.13^{\circ}[/tex]

The first and second order angles for light of wavelength 400 nm are [tex]23.58^{\circ}[/tex] and [tex]53.13^{\circ}[/tex].

[tex]\lambda=700\ \text{nm}[/tex]

m = 1

[tex]\theta=\sin^{-1}\dfrac{1\times 700\times 10^{-9}}{10^{-6}}\\\Rightarrow \theta=44.43^{\circ}[/tex]

m = 2

[tex]\theta=\sin^{-1}\dfrac{2\times 700\times 10^{-9}}{10^{-6}}[/tex]

Here [tex]\dfrac{2\times 700\times 10^{-9}}{10^{-6}}=1.4>1[/tex] so there is no second order angle for this case.

The first order angle for light of wavelength 700 nm are [tex]44.43^{\circ}[/tex].

Second order angle does not exist.

A 38.0 kg box initially at rest is pushed 4.00 m along a rough, horizontal floor with a constant applied horizontal force of 130 N. If the coefficient of friction between box and floor is 0.300, find the following. (a) the work done by the applied force J (b) the increase in internal energy in the box-floor system due to friction J (c) the work done by the normal force J (d) the work done by the gravitational force J (e) the change in kinetic energy of the box J (f) the final speed of the box m/s

Answers

Answer:

a)  Wapp = 520 N

b)  ΔUf = 447 N

c) Wn = 0

d) Wg = 0

e) ΔK = 73 J

f) v = 1.96 m/s

Explanation:

a)

Applying the definition of work, as the dot product between the applied force and the displacement, since both are parallel each other, the work done on the box by the applied force can be written as follows:

       [tex]W_{app} = F_{app} * \Delta X = 130 N * 4.0 m = 520 N (1)[/tex]

b)

The change in the internal energy due to the friction, is numerically equal to the work done by the force of friction.This work is just the product of the kinetic force of friction, times the displacement, times the cosine of the angle between them.As the friction force opposes to the displacement, we can find the work done by this force as follows:

       [tex]W_{ffr} = F_{fr} * \Delta X * cos (180) (2)[/tex]

The kinetic force of friction, can be expressed as the product of the kinetic coefficient of friction times the normal force.If the surface is level, this normal force is equal to the weight of the object, so we can write (2), as follows:

       [tex]W_{ffr} = F_{fr} * \Delta X * cos (180) = -\mu_{k} * m* g* \Delta X = \\ -0.300*38.0kg9.8 m/s2*4.0m = -447 J (3)[/tex]

So, the increase in the internal energy in the box-floor system due to the friction, is -Wffr = 447 J

c)

Since the normal force (by definition) is normal to the surface, and the displacement is parallel to the surface, no work is done by the normal force.

d)

Since the surface is level, the displacement is parallel to it, and the gravitational force is always downward, we conclude that no work is done by the gravitational force either.

e)

The work-energy theorem says that the net work done on the object, must be equal to the change in kinetic energy.We have two forces causing net work, the applied force, and the friction force.So the change in kinetic energy must be equal to the sum of the work done by both forces, that we found in a) and b).So, we can write the following expression:

        [tex]\Delta K = W_{app} + W_{ffr} = 520 J - 447 J = 73 J (4)[/tex]

f)

Since the object starts at rest, the change in kinetic energy that we got  in e) is just the value of the final kinetic energy.So, replacing in (4), we finally get:

       [tex]\Delta K = 73 J = \frac{1}{2}*m*v^{2} (5)[/tex]

Solving for v:[tex]v_{f} = \sqrt{\frac{2*\Delta K}{m} } = \sqrt{\frac{2*73J}{38.0kg}} = 1.96 m/s (6)[/tex]

a) The work done by the applied force   [tex]W_{AP}=520\ J[/tex]

b) The change in the internal energy [tex]\Delta U=447\ J[/tex]

c) Work done by normal force  [tex]W_n=0[/tex]

d) Work done by gravitation   [tex]W_g=0[/tex]  

e) The change in KE will be [tex]\Delta KE=73\ J[/tex]

f) The final speed v = 1.96 m/s

What will be the work done?

The work done on any object can be defined as the force applied on the object and its displacement due the effect of the force.

If the object achieve movement due to the work then the energy in the object will be kinetic energy.

If the object attains some height  against the gravity then the energy in the object will be potential energy.

Now it is given in the question that

The horizontal force   [tex]F_h=130\N[/tex]

mass of the object  m= 38 kg

Coefficient of friction [tex]\mu=0.3[/tex]

Displacement of the object [tex]\delta x=4\ m[/tex]

(a) The work done will be

[tex]W=F_h\tines \Delta x[/tex]

[tex]W=130\times 4=520\ J[/tex]

(b) The increase in the internal energy

The increase in the internal energy of the box is due to the energy generated by the force of friction so

[tex]W_f=F_f\times \Delta x\times Cos(180)[/tex]

here  [tex]F_f[/tex] is the frictional force and is given as

[tex]\mu=\dfrac{F_f}{R}[/tex]

Here R is the normal reaction and its value will be weight of the box in opposite direction.

[tex]\mu=\dfrac{F_f}{-mg}[/tex]

[tex]F_f=-mg\times \mu[/tex]

[tex]W_f=F_f\times \Delta x\times Cos180=-mg\times\mu \times cos180[/tex]

[tex]W_f=-38\times 9.81\times 0.3\times4=-447\J\ J[/tex]

(c) The work done by the normal force will be zero because the displacement is horizontal against the normal work so the work done will be zero.

(d) The work done by the gravitational force will also be zero. Because the displacement is horizontal and the gravitational force acts downward.

(e) The change in the KE of the box.

The change in the KE of the box will be the net energy of the box so from the work energy theorem the net energy will be

[tex]\Delta KE =W_{AP}-W_f=520-447=73\ J[/tex]

(f) The speed of the box

The KE of the box will be

[tex]KE=\dfrac{1}{2} mv^2[/tex]

[tex]v=\sqrt{ \dfrac{2\times KE}{m}[/tex]

[tex]v=\sqrt{\dfrac{2\times73}{38} }=1.96\ \dfrac{m}{s}[/tex]

Thus

a) The work done by the applied force   [tex]W_{AP}=520\ J[/tex]

b) The change in the internal energy [tex]\Delta U=447\ J[/tex]

c) Work done by normal force  [tex]W_n=0[/tex]

d) Work done by gravitation   [tex]W_g=0[/tex]  

e) The change in KE will be [tex]\Delta KE=73\ J[/tex]

f) The final speed v = 1.96 m/s

To know more about Work and energy follow

https://brainly.com/question/25959744

A uniform-density 7 kg disk of radius 0.20 m is mounted on a nearly frictionless axle. Initially it is not spinning. A string is wrapped tightly around the disk, and you pull on the string with a constant force of 42 N through a distance of 0.9 m. Now what is the angular speed

Answers

Answer:

The angular speed is 23.24 rad/s.

Explanation:

Given;

mass of the disk, m = 7 kg

radius of the disk, r = 0.2 m

applied force, F = 42 N

distance moved by disk, d = 0.9 m

The torque experienced by the disk is calculated as follows;

τ = F x d = I x α

where;

I is the moment of inertia of the disk = ¹/₂mr²

α is the angular acceleration

F x r = ¹/₂mr² x α

The angular acceleration is calculated as;

[tex]\alpha = \frac{2Fr}{mr^2} \\\\\ \alpha = \frac{2F}{mr}\\\\\alpha = \frac{2 \times 42 }{7 \times 0.2} \\\\\alpha = 60 \ rad/s^2[/tex]

The angular speed is determined by applying the following kinematic equation;

[tex]\omega _f^2 = \omega_i ^2 + 2\alpha \theta[/tex]

initial angular speed, ωi = 0

angular distance, θ = d/r = 0.9/0.2 = 4.5 rad

[tex]\omega _f^2 = 2\alpha \theta\\\\\omega _f = \sqrt{2\alpha \theta} \\\\\omega _f = \sqrt{2 \times 60 \times 4.5} \\\\\omega _f = 23.24 \ rad/s[/tex]

Therefore, the angular speed is 23.24 rad/s.

(will give brainliest to whoever answers first and explains reasoning) A 10kg object is spun around in a circle with a centripetal acceleration of 3.5m/s^2. What is the centripetal force acting on the object?

Answers

Answer:

35 N

Explanation:

F = ma

centripetal force = 10(3.5) = 35 N

If it takes 560 joules of work to move an object 10 meters what force was needed

Answers

Answer:

F = 56 N

Explanation:

Assuming that the applied force is parallel to the displacement, according to the definition of work, we can write the following expression for the force required:

       [tex]F = \frac{W}{\Delta x} =\frac{560J}{10m} = 56 N (1)[/tex]

a cohesive force between the liquids molecules is responsible for the fluids is called​

Answers

Answer:

static force

Explanation:

mark me brainliest

prove that d1=R(d1-d2) in relative density​

Answers

You know I’m going to be honest I don’t feel like it

1
Select the correct answer.
Which type of energy is thermal energy a form of?
A
chemical energy
B.
kinetic energy
C. magnetic energy
D. potential energy
Reset
Next

Answers

Answer:

B. kinetic energy

Explanation:

Thermal energy (It’s a low form of energy ) is a form of kinetic energy as it is produced as a result of motion of particles either if they vibrate at their position or they move along longer paths.

(5 Points)
a) At ground level, the pressure of the helium in a balloon is 1x105
Pa. The volume occupied by the helium is 9.6m The balloon is
released and it rises quickly through the atmosphere. Calculate
the pressure of the helium when it occupies a volume of 12m3.
(3 Marks)
b) A box is 15m below the surface of the sea. The density of sea-
water is 1020 kg/m.
Calculate the pressure on the box due to the sea-water.
(2 Marks)

Answers

Answer:

1. [tex]P_{2}[/tex] = 8 x [tex]10^{4}[/tex] Pa

2. P = 1.5 x [tex]10^{5}[/tex] N/[tex]m^{2}[/tex]

Explanation:

1. From Boyles' law;

[tex]P_{1}[/tex][tex]V_{1}[/tex] = [tex]P_{2}[/tex][tex]V_{2}[/tex]

[tex]P_{1}[/tex] = 1 x [tex]10^{5}[/tex] Pa

[tex]V_{1}[/tex] = 9.6 [tex]m^{3}[/tex]

[tex]V_{2}[/tex] = 12 [tex]m^{3}[/tex]

Thus,

1 x [tex]10^{5}[/tex] x 9.6 =  [tex]P_{2}[/tex] x 12

 [tex]P_{2}[/tex] = [tex]\frac{100000 x 9.6}{12}[/tex]

     = 80000

[tex]P_{2}[/tex] = 8 x [tex]10^{4}[/tex] Pa

2. Pressure, P = ρhg

where: ρ is the density of the fluid, h is the height/ depth and g is the acceleration due to gravity (9.8 m/[tex]s^{2}[/tex]).

Thus,

P = 1020 x 15 x 9.8

  = 149940

P = 1.5 x [tex]10^{5}[/tex] N/[tex]m^{2}[/tex]

A motorist is driving at 15 m/s when she sees that a traffic light 315m ahead has just turned red. She knows that this light stay red for 25 s, and she wants to be 20 m from the ligt when it turns green again. Taht way, she will still be able to stop if the light stays red longer than expected. She applies the brake gradually such that her acceleration is ax(t)= c + bt, where c and b are constant. Assume she starts with a constant speed at the origin.

Find the values of c a b and any other unknown constants in order to answer the following questions.

1. Given the motorist's acceleration as a function of time, what are her position and velocity fucntions? - Do not use numbers for any constant here. Only derive the position and velocity functions.

2. What is her speed as she reaches the light?

Answers

Answer:

1)   x = x₀ + vot - ½ c t² - 1/6 bt³,    v = v₀ - ct - ½ b t²

2)   v₁ = 5.25 m/s,         v₂ = -8 m/s

Explanation:

1) For this exercise, the relationship of the body is not constant, so you must use the definition of speed and position to find them.

acceleration is

           a = c + bt

a) the relationship between velocity and acceleration

           a = [tex]\frac{dv}{dt}[/tex]

           dv = -a dt

The negative sign is because the acceleration is contrary to the speed to stop the vehicle.

we integrate

           ∫ dv = - ∫ a dt

           ∫ dv = -∫ (c + bt) dt

            v = -c t - ½ b t²

This must be valued from the lower limit, the velocity is vo, up to the upper limit, the velocity is v for time t

             v - v₀ = -c (t-0) - ½ b (t²-0)

             v = v₀ - ct - ½ b t²

b) the velocity of the body is

             v = [tex]\frac{dx}{dt}[/tex]

             dx = v dt

we replace and integrate

              ∫ dx = ∫ (v₀ - c t - ½ bt²) dt

              x-x₀ = v₀ t - ½ c t² - ½ b ⅓ t³

Evaluations from the lower limit the body is at x₀ for t = 0 and the upper limit the body is x = x for t = t

           x - x₀ = v₀ (t-0) - ½ c (t²-0) + [tex]\frac{1}{6}[/tex]  (t³ -0)

 

           x = x₀ + vot - ½ c t² - 1/6 bt³

2) The speed when you reach the traffic light

Let's write the data that indicates, the initial velocity is vo = 15 m / s, the initial position is xo = 315m, let's use the initial values ​​to find the constants.

       t = 25 s x = 20

we substitute

          20 = 315 + 15 25 - ½ c 25² - 1/6 b 25³

         0 = 295 + 375 - 312.5 c - 2604.16 b

         670 = 312.5 c + 2604.16 b

we simplify

         2.144 = c + 8.33 b

Now let's use the equation for velocity,

        v = v₀ - ct - ½ b t²

        v = 15 - c 25 - ½ b 25²

        v = 15 - 25 c - 312.5 b

               

let's write our two equations

        2.144 = c + 8.33 b

        v = 15 - 25 c - 312.5 b

Let's examine our equations, we have two equations and three unknowns (b, c, v) for which the system cannot be solved without another equation, in the statement it is not clear, but the most common condition is that if the semaphore does not change, it follows with this acceleration (constant) to a stop

               a = c + b 25

from the first equation

              c = 8.33 / 2.144 b

              C = 3.885 b

we substitute in the other two

            v = 15 - 25 (3.885 b) - 312.5 b

            v = 15 - 409.6 b

final acelearation

            a = 28.885 b

           

let's use the cinematic equation

               [tex]v_{f}^2[/tex]= v² - 2 a x

                0 = v² - 2a 20

               0 = v² - (28.885b) 40

               v² = 1155.4 b

we write the system of equations

               v = 15 - 409.6 b

               v² = 1155.4 b

resolve

              v²= 1155.4 ( [tex]\frac{15 -v }{409.6}[/tex] )

              v² = 2.8 ( 15 -v)

              v² + 2.8 v - 42.3 = 0

              v=  [ -2.8 ±[tex]\sqrt {2.8^2 + 4 \ 42.3) }[/tex] ]/2 = [-2.8 ± 13.3]/2

              v₁ = 5.25 m/s

              v₂ = -8 m/s

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