Civil engineers calculate suggested speeds around corners (those yellow signs) when designing roads based upon the ability of a car to remain upon the road. The ability of the car to remain upon the road when taking a corner is determined by the centripetal acceleration of your car around the corner. If you are driving a car around a flat circular turn with a suggested speed of 15 mph, how much more likely is it that your car does not successfully take the corner (ends up in the ditch) if you were to instead drive 45 mph? Cite an equation to back up your thinking.​

Answers

Answer 1

The car shall not be successful since the corner must have a radius as nine times as the real corner designed for a suggested speed of 15 miles per hour.

By definition of centripetal acceleration, the square of the velocity taken by the vehicle (\(v\)), in miles per hour, is directly proportional to the radius of the corner (\(R\)), in meters. Then, we have the following relationship:

\(\frac{v_{A}^{2}}{R_{A}} = \frac{v_{B}^{2}}{R_{B}}\) (1)

Where:

\(v_{A}\) - Suggested velocity.\(v_{B}\) - Real velocity. \(R_{A}\) - Real radius of the corner.\(R_{B}\) - Expected radius of the corner.

If we know that \(v_{A} = 15\,\frac{mi}{h}\), \(v_{B} = 45\,\frac{mi}{h}\) and \(R_{A} = k\), then the expected radius of the corner is:

\(R_{B} = k\cdot \left(\frac{v_{B}}{v_{A}} \right)^{2}\)

\(R_{B} = 9\cdot k\)

In order to successfully take a corner at 45 miles per hour, the corner must have a radius as nine times as the real corner designed for a suggested speed of 15 miles per hour. Thus, the car shall not be successful at a speed of 45 miles per hour.

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Related Questions

Which of the following industries is the largest producer of primary air pollutants in the United States?

Answers

The largest producer of primary air pollution in the United States is what? electricity producing plants.

Answer:

electricity production

Explanation:

Two resistors, 20 ohms and 30 ohms, are connected in parallel. This combination is connected in a series to an 8 ohms resistor and a battery of e.m.f. 12 volts. What is the current along 20 ohms?

Answers

Ohm's law is a fundamental principle in physics and electrical engineering that relates the current flowing through a conductor to the voltage applied across it. It states that the current (I) passing through a conductor is directly proportional to the voltage (V) across the conductor, and inversely proportional to the resistance (R) of the conductor.

The current along 20 ohms in a circuit with two resistors, 20 ohms and 30 ohms, which are connected in parallel, and this combination is connected in a series to an 8 ohms resistor and a battery of e.m.f. 12 volts can be calculated as follows: The equivalent resistance for the two resistors connected in parallel by using the formula 1/Rt = 1/R1 + 1/R2, where R1 and R2 are the resistors in parallel.1/Rt = 1/20 + 1/30 = 3/60 + 2/60 = 5/60Rt = 60/5 = 12 ohms.

The equivalent resistance of the two parallel resistors is 12 ohms.

Now, calculate the total resistance of the circuit by adding the equivalent resistance of the parallel resistors and the 8 ohms resistor.

Rtotal = 12 + 8 = 20 ohmsThe total resistance of the circuit is 20 ohms.

Finally, calculate the current along the 20 ohms resistor using Ohm's law, which states that I = V/R, where V is the voltage of the battery and R is the resistance. I = V/R = 12/20 = 0.6 A.

The current along the 20 ohms resistor is 0.6 A.

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Trace the changes that take place in a flower from gamete formation to fruit

formation.

5

36 In the given circuit, A, B, C and D are four lamps connected with a battery of

60V.

Analyse the circuit to answer the following questions.

(i) What kind of combination are the lamps arranged in (series or parallel)?

(ii) Explain with reference to your above answer, what are the advantages (any

two) of this combination of lamps?

(iii) Explain with proper calculations which lamp glows the brightest?

(iv) Find out the total resistance of the circuit.​

Answers

Pollination is the transfer of pollen for plant fertilization

The correct responses are as follows;

The description of the changes that take place is included in this response

6 (i) The circuit arrangement is a parallel circuit arrangement

(ii) The advantages are;

Brighter bulbsHigher uptime of the bulbs

(iii)  Lamp C glows the brightest

(iv) The total resistance is 4 Ω

The reason roe the above responses are as follows:

During the course of pollination, the pollen, through movement, finds it way to the germ-cell in the female ovary, where it fuses with the female egg (gamete) located inside the ovule

The resulting fertilization produces the zygote, which forms an embryo inside the ovule by dividing several times

A seed is formed from the ovule when it develops a tough coat, and by rapid growth a fruit is formed as the ovary matures

5 (i) The kind of combination, where all the wires that enters the bulb are joined on one side of the bulbs, and all the wires that comes from the bulbs are joined on the other end of the bulb, before joining the circuit is a parallel connection

(ii) The advantages of bulbs connected in parallel are;

The voltage available in the power source reaches all the bulbs. That is each bulb had the voltage of the power source across it and therefore, is brighter than   when the bulbs are arranged in seriesOther bulbs remain functional following the disconnection of one of the bulbs or loops

(iii) The bulb that glows brightest is given by the bulb that consumes the most energy per unit time, and therefore, the bulb that has the most power

Power consumed by each bulb is given as follows;

Bulb A, \(P_A\) = 3 A × 60 V = 180 W

Bulb B, \(P_B\) = 4 A × 60 V = 240 W

Bulb C, \(P_C\) = 5 A × 60 V = 300 W

Bulb D, \(P_D\) = 3 A × 60 V = 240 W

The highest power used by a bulb is 300 W, by bulb C

Therefore;

Bulb C is the brightest bulb

(iv) The total resistance of the circuit is given as follows;

\(Total \ resistance =\dfrac{Circuit \ voltage}{Total \ current}\)

Total current, \(I_{tot}\) = 3 A + 4 A + 5 A + 3 A = 15 A

Circuit voltage, V = 60 V (Given)

Therefore, we have;

\(Total \ resistance =\dfrac{60 \, V}{15 \, A} = 4 \, \Omega\)

The total resistance is 4 Ω

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Trace the changes that take place in a flower from gamete formation to fruit formation.536 In the given

how many mg does a 433 kg sample contain? a) 4.33 × 10-4 mg b) 4.33 × 107 mg c) 4.33 × 10-3 mg d) 4.33 × 106 mg e) 4.33 × 108 mg

Answers

Given, the mass of the sample = 433 kg. We need to find the mass of the sample in milligrams (mg).

1 kilogram (kg) = 1,000,000 milligrams (mg)

Therefore,

Mass of the sample in mg = 433 × 1,000,000 mg = 4.33 × 10^8 mg.Hence, the answer is an option (e) 4.33 × 10^8 mg.

The conversion factor between kilograms and milligrams is 1 kg = 1,000,000 mg. Therefore, to convert the mass of the sample from kilograms to milligrams, we simply multiply it by 1,000,000.

433 kg × 1,000,000 mg/kg = 433,000,000 mg

To express the result in scientific notation, we write it as 4.33 × 10^8 mg.

Option (e) is the correct answer.

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a 1500kg ferry boat has a momentum of 25000 kg-m/a. What is the speed of the ferry boat

Answers

The speed of the ferry boat is 16.67 meters per second.

The Pythagorean theorem is what?

At a velocity of 10.0 m/s, the boat crossed the calm sea. Un = 2.00 m/s, river water speed Let v represent the ferry's effective river crossing speed, allowing it to travel directly to the location on the opposite side. We can then express their velocities as shown below.

What made Pythagoras well-known?

Greek philosopher Pythagoras made significant contributions to mathematics, astronomy, and music theory. Although the Babylonians were aware of the theorem 1000 years before Pythagoras, he may be the first to use it.

We can use the formula for momentum:

p = mv

where p is momentum, m is mass, and v is velocity or speed.

Rearranging this formula to solve for velocity, we get:

v = p/m

Substituting the given values, we get:

v = 25000 kg-m/s / 1500 kg

v = 16.67 m/s

Therefore, the speed of the ferry boat is 16.67 meters per second.

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The conductance of a wire varies directly as the square of the wire's diameter and inversely as its
length. Fifty meters of wire with diameter 2 mm has conductance 0.12 mho (unit of conductance).
If a wire of the same material has length 75 m and diameter 2.5 mm, what is its conductance?

Answers

Since it varies directly with the square of the wire's diameter and inversely with wire length, the conductance of a wire is 0.15 mho.

Does a wire's electrical resistance change inversely with its square of diameter and directly with its length?

A wire's electrical resistance varies inversely as the square of its diameter and directly as its length. A wire with a diameter of 1/4 inch and a length of 200 inches has a 20 ohm resistance.

Let L be the wire's length, d its diameter, and C its conductance be the parameters.

Based on the facts provided, we can:

C ∝ d² (conductance varies directly as the square of the diameter)

C ∝ 1/L (conductance varies inversely as the length)

Combining these two proportionalities, we get: C ∝ d²/L

This connection can be used to find a solution to the issue. Using the numbers for the 50 m wire, we can first calculate the proportionality constant as follows:

C = k(d²/L)

0.12 = k(2²/50)

k = 0.12*50/4 = 1.5

So, using this value of k, we can determine the conductance of a 75 m wire with a 2.5 mm diameter:

C = k(d²/L)

C = 1.5*(2.5²/75)

C = 0.15 mho

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Please helpp !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Please helpp !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

B. a car on a track, a stop watch, and a ruler

Kelly does 600 J of work as the pushes a cow on roller skates. if she pushes the cow 4 meters away, how much force was Kelly pushing with?

Answers

To calculate the force Kelly was pushing with, we can use the equation:

Work (W) = Force (F) × Distance (d)

Given that Kelly does 600 J of work and pushes the cow 4 meters away, we can rearrange the equation to solve for force:

F = W / d

Plugging in the values, we get:

F = 600 J / 4 m

F = 150 N

Therefore, Kelly was pushing with a force of 150 Newtons.

12. A screwdriver is which type of a simple machine?
O wedge
O screw
O wheel and axle
O lever

Answers

Answer:

wheel and axle

Explanation:

hope this helps

4. A racing car has a uniform acceleration of 4 m s - '2. What distance will it cover in 10 s after start?

Answers

Answer:

200 m

Explanation:

Initial velocity- 0

final velocity= v

time= 10 seconds

to find final velocity

v= u + at

v= 0 + 4*10

v= 0 + 40

v= 40 m/s

to find distance

s= ut + 1/2at²

s= 0*10 + 1/2*4*(10)²

s= 1/2 *4*100

s=200m

answer : 200 m

Which is easier for a beginner? (This is for archery)

O long bow

O recurve bow

Answers

Answer:

The recurve bows

Explanation:Vote brainliest plz

The recurve bow is smaller and easier to handle while the longbow is used more for competitions. So I would say the recurve bow is easier for a beginner

the temperature of a 2.0 kg block increases by 5 degrees celsius when 2000j of thermal energy are added to the block. what is the specific heat of the block?

Answers

Specific heat is quantity of heat required to increase the temperature of a substance by one degree celsius.

The formula to calculate heat energy is

Q=mc∆T

How to calculate specific heat capacity using heat energy formula?

We know, Q=mc∆T

Where Q = heat energy

m = mass

c= specific heat capacity

∆T= change in temperature

Thus,

According to above formula

c= Q/m∆T

Here m= 2 kg

∆T= 5 degrees

Q= 2000 joules

c= 2000/2×5

c= 200

Thus, the specific heat capacity of the block is 200.

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what is the pressure when a liquid is boiling at its normal boiling point?

Answers

The normal boiling point of a liquid is the temperature at which its vapor pressure is equal to one atmosphere (760 torr).

A scientist designed an experiment to test the effect of temperature on bacterial growth. He grew three different cultures of the bacterium E. coli under three heat lamps at different temperatures.

Write a hypothesis that he may be testing​

Answers

Answer:

Depending on the tempetures he's most likly looking to see what temp it will grow under and which one grows the fastest

Explanation:

Answer:

Depending on the tempetures he's most likly looking to see what temp it will grow under and which one grows the fastest

Explanation:

A socond baseman tosses the ball to the first basoman, who catches 4 at the same level from which in was thrown. The throw Part A is miede with an initial spood of 18.0 m/s at an angle of 31.0

What is the horizontal component at tre balis velocity just before in is caight? abdue the horizontal. Part B How bon as the balin the an?

Answers

To solve this problem, we need to analyze the projectile motion of the ball. Therefore, the horizontal component is approximately 14.878 m/s.Therefore, the ball is in the air for approximately 1.954 seconds.

Given:

Initial speed (magnitude): 18.0 m/s

Launch angle: 31.0 degrees above the horizontal

We can break down the initial velocity into horizontal and vertical components:

Initial horizontal velocity (v₀x) = v₀ * cos(θ)

Initial vertical velocity (v₀y) = v₀ * sin(θ)

where v₀ is the initial speed and θ is the launch angle.

Using the given values:

v₀ = 18.0 m/s

θ = 31.0 degrees (converted to radians, 31° * π/180 ≈ 0.5411 rad)

v₀x = 18.0 m/s * cos(0.5411 rad) ≈ 14.878 m/s (rounded to three significant figures)

v₀y = 18.0 m/s * sin(0.5411 rad) ≈ 9.570 m/s (rounded to three significant figures)

Part A: The horizontal component of the ball's velocity just before it is caught is equal to the initial horizontal velocity because there is no horizontal acceleration during the ball's flight. Therefore, the horizontal component is approximately 14.878 m/s.

Part B: The time of flight can be determined using the equation:

Δy = v₀y * t + (1/2) * g * t²

where Δy is the vertical displacement (initially 0 m since it is caught at the same level), v₀y is the initial vertical velocity, t is the time, and g is the acceleration due to gravity (-9.8 m/s²).

0 m = 9.570 m/s * t + (1/2) * (-9.8 m/s²) * t²

Simplifying the equation:

-4.9 t² + 9.570 t = 0

Solving this quadratic equation, we find two possible solutions for t: t = 0 s or t = 1.954 s.

Since the ball is caught, we consider the positive value of time, which is approximately t = 1.954 s (rounded to three significant figures).

Therefore, the ball is in the air for approximately 1.954 seconds.

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Hurricanes that hit the east coast of the United States often start as low-pressure systems off the west coast of Africa. Which global winds move these hurricanes toward the United States?

A.
polar easterlies

B.
prevailing westerlies

C.
northeast trade winds

D.
southeast trade winds

Answers

Hurricane propagation is the process through which a hurricane moves from one location to another.

Winds from throughout the world direct hurricanes. The environmental wind field, commonly referred to as the dominant winds, is what directs a cyclone along its course. The hurricane moves in the direction of this wind field, which affects the hurricane's speed of movement.

The northeast trade winds move these hurricanes toward the United States.

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Pls I need help ASAP

Pls I need help ASAP

Answers

Answer:

i dont undertsnad what do u ned hep wit?

Explanation:

Sound waves...
I. travel in a vacuum
II. are invisible
III. move through water

OI and II

O I and III

O I, II, and III

O II and III

Answers

Answer:

Option 3

Explanation:

Hope it will help you

Pls Mark me as brainliest

You tmuc

Sound waves are invisible and can move through the water, therefore the correct answer is option D.

What is a sound wave?

It is a particular variety of mechanical waves made up of the disruption brought on by the movements of the energy. In an elastic medium like the air, a sound wave travels through compression and rarefaction.

Sound waves cannot travel in a vacuum, and they are invisible in nature.

While electromagnetic waves are transverse waves, sound waves are longitudinal waves, and the temperature of the medium in which they travel greatly affects the speed of the sound.

The mathematical expression for the speed of the sound in air is given by

v= √γRT

where v is the speed of the sound

R is the ideal gas constant

T is the temperature

γ is the adiabatic index

The speed of sound in air at 0° Celcius is 330 m/s.

Since sound waves can travel through water and are invisible, option D is the appropriate answer.

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Thirty-five coulombs of charge flow through a wire in 2 minutes. determine the current in the wire.

Answers

Thirty-five coulombs of charge flow through a wire in 2 minutes accounts for around 0.29167 amperes in the current wire.

Given:

Electric charge= 30 coulomb

Time for which charge flows through a wire = 2 minutes = 120 seconds

To find:

Electric current flowing in a wire=?

To calculate electric current understand the concept:

An electric current is the flow of charged particles through the conducting material.

The Standard International unit of electric current is Ampere or amp or A.

One ampere is defined as the flow of one-coulomb electric charge in one second.

It can be calculated as follows:

Electric current (Ampere) = Electric charge(Coulomb) ÷ time(seconds)

Electric current (A) = 35 C ÷ 120 s

Electric current = 0.29167 amperes

Hence, the electric current is flowing at the rate of 0.29167C/s or 0.29167 Ampere through a wire.

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blank is a wave that remains in a constant position

Answers

A wave that remains in a constant position is referred to as a stationary wave or a standing wave.

It is formed by the superposition of two waves with the same frequency and amplitude traveling in opposite directions. Unlike a traveling wave that moves through space, a standing wave appears to be stationary because the wave peaks and troughs oscillate in place.

The formation of a standing wave occurs when a wave reflects back upon itself, interacting constructively and destructively with the incoming wave. This phenomenon is characterized by the presence of nodes and antinodes. Nodes are points along the wave where the amplitude is always zero, resulting from destructive interference between the two waves. Antinodes, on the other hand, are points of maximum displacement, created by constructive interference..

Standing waves have significant implications in various fields of study. In physics and engineering, they are essential in the analysis of acoustics, optics, and electromagnetic fields. They find applications in musical instruments, where standing waves inside the instrument's resonating body create distinct harmonics and produce specific musical tones.

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I need help

please help me with this​

I need helpplease help me with this

Answers

Djdjjdjdjdjjfjfhshdhehe

a negatively charged ion​

Answers

a negatively charged ion is a anion

Define electroplating

Answers

Answer:

La galvanoplastia o electrodeposición es una aplicación práctica de la electroquímica. Se trata de una técnica basada en los principios electroquímicos, en donde se aplica una o varias capas de un metal seleccionado sobre un objeto receptor, por lo general, también metálico.

Explanation:

Espero te sirva de algo ;)

Gold-198 has a half-life of 2.7 days. Complete the table for an initial sample size of 200 grams

Answers

25.1 grams are still present after 8.1 days. When the Gold-198 has a half-life of 2.7 days.

What is radioactivity?

The act of producing radiation spontaneously is known as radioactivity. This is accomplished by an unstable atomic nucleus that wants to give up some energy in order to move to a more stable form.

The half-life of the gold  =2.7 days

Sample size  = 200 grams

N is the left amount after the given time =?

Constant of rate = 0.26

The rate constant is found as;

\(\rm \lambda = \frac{0.693}{t^{\frac{1}{2}}} \\\\ \lambda = 0.256 \ days^{-1}\)

The amount after the given time;

\(\rm N=N_0 \times e^{-\lambda t} \\\\\ N = 200 \times e^{-0.256 \times 8.1 \ days} \\\\N=25.1 \ gm\)

Hence,25.1 grams are still present after 8.1 days.

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Explain some endless capabilities of our vast universe?

Answers

ANSWER:

STEP-BY-STEP EXPLANATION:

Answer:

It is impossible to answer that as we could discover more than we know now in years to come with advanced technologies

Explanation:

Three materials, put them in order of what
light does when it hits them.
clay, shiny dimes, eyeglasses

Three materials, put them in order of whatlight does when it hits them.clay, shiny dimes, eyeglasses

Answers

Answer:

it's a

Explanation:

hope this helps!!!!!!

Find the rate of change of the volume of a cube with respect to the length of its side when =11

Answers

When s = 11, the rate of change of the volume of the cube with respect to the length of its side is 363 cubic units per unit change in side length.

To find the rate of change of the volume of a cube with respect to the length of its side, we need to differentiate the volume formula with respect to the side length.

Let's denote the side length of the cube as "s" and the volume as "V."

The volume of a cube is given by the formula V = s³.

To find the rate of change of V with respect to s, we differentiate V with respect to s:

dV/ds = 3s².

Now, if we substitute s = 11 into the expression, we can find the rate of change at that specific value:

dV/ds = 3(11)²

      = 3(121)

      = 363.

Therefore, when s = 11, the cube's volume changes at a rate of 363 cubic units for every unit increase or decrease in side length.

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Rank the main causes of death among young children, from the highest incidence to the lowest incidence. ____

Answers

Unintentional injuries caused by accidents are the number one killer of children and teenagers.

What causes the majority of adolescent deaths?

A little over half of all adolescent fatalities are caused by accidents. Over one-third of all fatal accidents fall under the category of motor vehicle fatalities, which is the top cause of death for teens. Non-Hispanic black male teens have the highest death rate.

The top causes of mortality for children under 5 years old continue to be congenital anomalies, pre-term birth complications, birth asphyxia, and other infectious diseases like pneumonia, diarrhea, and malaria. According to a recent study, homicide is the top cause of death for children in the United States, and the total rate has grown by 4.3% annually on average.

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Four 1.50-V cells are connected in series to a 12.0-Ω lightbulb. If the resulting current is 0.45 A, what is the internal resistance of each cell, assuming they are identical and neglecting the resistance of the wires?

Answers

Four 1.50-V cells are connected in series to a 12.0-Ω lightbulb. If the resulting current is 0.45 A, The internal resistance of each cell, assuming they are identical and neglecting the resistance of the wires is 1.33 Ω.

To determine the internal resistance of each cell, we can use Ohm’s law and the concept of voltage division in a series circuit. Ohm’s law states the relationship between electric current and potential difference. The current that flows through most conductors is directly proportional to the voltage applied to it. Georg Simon Ohm, a German physicist was the first to verify Ohm’s law experimentally.

In a series circuit, the total voltage across the circuit is the sum of the individual voltages. Since four 1.50-V cells are connected in series, the total voltage across the circuit is:

Total voltage = 4 x 1.50 V = 6.00 V

The total resistance in the circuit is the sum of the lightbulb resistance and the internal resistance of the cells:

Total resistance = Lightbulb resistance + Internal resistance of each cell = 12.0 Ω

The current flowing through the circuit is given as 0.45 A.

Using Ohm’s law, we can calculate the voltage drop across the internal resistance of each cell:

Voltage drop across each internal resistance = Total voltage – Voltage across the lightbulb

= 6.00 V – (0.45 A x 12.0 Ω)

= 6.00 V – 5.40 V

= 0.60 V

Now, we can determine the internal resistance of each cell using Ohm’s law: Internal resistance of each cell = Voltage drop across each internal resistance / Current

= 0.60 V / 0.45 A

= 1.33 Ω

Therefore, assuming the cells are identical and neglecting the resistance of the wires, the internal resistance of each cell is approximately 1.33 Ω.

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2. You push a 12.3-kg shopping cart with a force of 10.1 N.
(a) What is the acceleration of the cart?
(b) If the cart starts from rest, how far does it move in 2.50 s?


Plz answer quick

Answers

Answer:

Explanation:

The important part about this problem is the acceleration, which you must find by using

F = ma,

where F is the force applied,

m is the mass,

and a is the acceleration.

F = ma

10.1 N = (12.3 kg)a

a = 0.8211 m/s^2

Now use the kinematics equations.

d = vot + (1/2)at^2

where d is the distance moved,

vo is the initial velocity (0),

a is the acceleration,

and t is the time.

d = vot + (1/2)at^2

d = (0 m/s)(2.5 s) + (1/2)(0.8211 m/s^2)(2.5 s)^2

d = 2.57 m

a. The acceleration of the cart, is 0.821 \(m/s^2\).

b. The car moved a distance of 30.63 meters starting from rest.

Given the following data:

Mass of shopping cart = 12.3 kgForce = 10.1 NInitial velocity, u = 0 m/s (since the cart is starting from rest). Time, t = 2.50 seconds.

a. To find the acceleration of the cart, we would apply Newton's Second Law of Motion:

Mathematically, Newton's Second Law of Motion is given by this formula;

\(Acceleration = \frac{Force}{Mass}\)

Substituting the given values, we have;

\(Acceleration = \frac{10.1}{12.3}\)

Acceleration = 0.821 \(m/s^2\)

Therefore, the acceleration of the cart, is 0.821 \(m/s^2\).

b. To find the distance covered by the shopping cart, we would use the second equation of motion.

Mathematically, the second equation of motion is given by the formula;

\(S = ut + \frac{1}{2} at^2\)

Where:

S is the distance covered. u is the initial velocity. a is the acceleration. t is the time measured in seconds.

Substituting the values into the formula, we have;

\(S = 0(2.5) + \frac{1}{2} (9.8)(2.5)^2\\\\S = 0 + 4.9(6.25)\)

Distance, S = 30.63 meters.

Therefore, the car moved a distance of 30.63 meters starting from rest.

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Other Questions
Genius PLC has grown rapidly since its stock market flotation five years ago. Despite its rapid growth the company has been able to finance all its new development from retained earnings and employs no debt in its capital structure. The companys earnings for the year that has just ended was 80 MILLION, a new high, and with 200 million shares outstanding this produced EPS (earnings per share) of 40p. Last year the company re-invested 80% of its earnings and recorded a rate of growth of earnings 32%, well above the minimum rate of return of 20% sought by investors in its sector of the market. Exactly this growth is also expected for next year for the earnings. The company has now opened stores in all the larger cities in the UK and new stores it plans to open will be located in towns with smaller markets that will produce lower turnover and profits per store. For the next 4 years or so it is anticipated that expansion will continue to be profitable, but less so than in the past even if the process is managed with the same degree of efficiency that has characterised the companys development over the last few years. As the coverage of the UK market becomes more complete it is planned to reduce the amount of annual investment. It is anticipated that the company will again invest 80% of its earnings next year, 60% of its earnings the following year and 40% the subsequent year. It is expected that the rate of return on new investment will fall to 35% next year, 30% the year after, and 25% three years from now. After the next three years management believes that there is unlikely to be scope for any investment offering internal rates of return of more than 20%. With the disappearance of opportunities for profitable growth it is intended in 4 years time to increase the dividends to 75% of earnings.a. Estimate the value of the company using both the dividend and earnings based models, as well as the current price of the companys shares. Set out the assumptions on which the models are based and discuss how appropriate they appear to be in this context. Determine the contribution of Growth opportunities to the estimated value of the company.b. How would the value of the company change if the required Rate of Return was 15% ? Alternatively if it was 25% ? Comment on your reply.c. Determine the expected price/earnings ratio today. Explain the determinants of the PE in reference to the two valuation models used.d. A member of the board suggests identifying an appropriate price-earnings ratio for Genius PLC and using this as a multiplier to derive a value for the company. Comment on this suggestion.e. The government issued a 15 year bond offering an interest rate of 12 per cent 10 years ago. Since then interest rates have fallen sharply. The bond now has five years to run to maturity and the government has just issued a five year bond offering an interest rate of 6 per cent. Determine a value for the bond that has five years to run to maturity, assume the bond has a face value of 100 and interest is paid annually. Explain your answer. Which two activities are examples of data collecting? PLS HELP DUE VERY SOONWrite an equation that represents the green line Help me See the picture Im giving brainliest Which is an example of money as a unit of account? Hi! I'm in 8th grade.. But I wnt to be a lawyer does anybody have any tips? What are the domain and range of the function fix) = x* - 2x2 - 4? Predict the nature of the indicated covalentbond.polar or non-polar HELP ME WITH THIS QUESTION PLS A principal receives reports from teachers via email. the probability model describes the number of emails the principal may receive in a day. emails received 0 1 2 3 4 5 p(x) 0.05 0.15 0.35 0.25 0.15 0.05 how many emails would you expect the principal to receive each day? (2 points) 3.9 3.65 3.25 2.9 2.45 What was one major outcome of the First Opium War?A. Great Britain and China formed a military alliance against Japan.B. Great Britain lost its influence over China's economic policies.C. China agreed to sell its valuable opium reserves to Great Britain.D. China was forced to surrender Hong Kong to Great Britain. Pls help!!!! will give brainly!!how to say in spanish:i need a blouse and leggings using the correct form of the verb necesitar. At a clover city council meeting, a plan to fund more sign language programs was presented. the reasoning behind the request was that less than 25% of parents with hearing-impaired children have the ability to pass a sign-language exam. if this is true, the council will agree to fund more programs for these parents. the council decides to take a 175-person volunteer sample of parents in clover city that have children with auditory issues and conduct a significance test for h0: p = 0.25 and ha: p < 0.25, where p is the proportion of these parents that can pass the sign language exam. they will perform the significance test at a significance level of ? = 0.05 for the hypotheses.part a: describe a type ii error that could occur. what impact could this error have on the situation?part b: out of the 175 volunteer parents of children with hearing problems, 54 passed, resulting in a p-value of 0.96. what can you conclude from this p-value given the data of the 175 parents is sufficient to perform a significance test for the hypotheses?part c: what possible defect in the study can you find in part b? explain What is the median between 75, 87, 82, 78 The mean of a set of data is 120.97 and its standard deviationis 18.27. Find the z score for a value of 80.15. The histograms display the frequency of temperatures in two different locations in a 30-day period.A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 14. A shaded bar stops at 10 above 60 to 69, at 9 above 70 to 79, at 5 above 80 to 89, at 4 above 90 to 99, and at 2 above 100 to 109. There is no shaded bar above 110 to 119. The graph is titled Temps in Sunny Town.A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 14. There is no shaded bar above 60 to 69. A shaded bar stops at 4 above 70 to 79, at 4 above 80 to 89, at 6 above 90 to 99, at 6 above 100 to 109 and at 10 above 110 to 119. The graph is titled Temps in Beach Town.When comparing the data, which measure of variability should be used for both sets of data to determine the location with the most consistent temperature? IQR, because Sunny Town is symmetric IQR, because Beach Town is skewed Range, because Sunny Town is skewed Range, because Beach Town is symmetric use the theory of evolution to explain the observation that there are no tussles males in the park why do males retain their tusks, when 50% of females lost them Select the best answer for the question.1. What art movement represents a movement by Black artists to reclaim their visual narrative?O A. RomanticismOB. SocialismOC. ImpressionismO D. The Harlem RenaissanceO How do I solve for X If I have a car, I ____to work