To find the rate at which the man and woman are moving apart, calculate the distance each has traveled and add their speeds since they are moving in opposite directions. The man traveled 2400 ft and the woman 3600 ft in their respective times, and the rate at which they are moving apart 15 minutes after the woman starts walking is 6 ft/s.
The student's question involves determining the rate at which two people are moving apart after a certain amount of time has passed, with one walking north and the other south from different starting points. To solve this, we can use the concept of relative velocity in one dimension, as the paths of the man and the woman are perpendicular to each other.
Firstly, we calculate the distance the man has walked in 20 minutes (since he started 5 minutes before the woman). At 2 ft/s, he would have walked 2 ft/s × 1200 s = 2400 ft north of point P. The woman, having started 5 minutes later, would have walked for 15 minutes at 4 ft/s, so she would have walked 4 ft/s × 900 s = 3600 ft south of her starting point.
When calculating the rate at which they are moving apart, we need to consider the sum of their speeds as they are moving in opposite directions. The man's speed is 2 ft/s and the woman's speed is 4 ft/s, so the rate at which they are moving apart is 2 ft/s + 4 ft/s = 6 ft/s.
what is the main difference between protons and neutrons
Answer: charges
Explanation: protons are positively charged while neutrons have no charge at all
Starting from rest, a ball of mass 2 kg experiences a constant force of 8 n. what is the final kinetic energy (in j) of the ball after it has traveled a distance of 8 m?
A ball is starting from the rest and has a mass of 2 kg, then the final kinetic energy of the ball that travelled to a distance of 8 m is 144.
What is Kinetic energy?An item or particle's motion gives it kinetic energy, which it might use to move. By exerting a net force on an item, work is done, which transfers energy; as a result, the object accelerates and obtains kinetic energy.
A moving item or particle's ability to move depends on both its mass and velocity. This is known as kinetic energy.
[tex]Force= Mass * Acceleration[/tex]
a=F/m
= 8 N / 2 kg= 4m/s²
Now find the final velocity,
[tex]v_f^2[/tex] = [tex]V_i[/tex]²+2ad
= 0²+(2) × (4) × (18) = 144
[tex]v_f^2[/tex] = √144
[tex]v_f[/tex] = 12
Now find the kinetic energy of the ball,
KE = 1/2 mv²
KE= (0.5) × (2) × (12)²
KE = 144
Therefore, the kinetic energy of the ball is 144.
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Use this excerpt from the text to answer the question. "Some people insist the United States is more properly called a republic rather than a democracy." The people who support this statement argue that the United States is a republic because in its government,
A dog sledding team is comprised of a 80.0 kg musher (the person driving the sled), a 21.0 kg sled and four dogs. assume each dog\'s pull is fully transmitted to the sled, applied parallel to the ground and the sled travels along level ground. how much power does each dog supply to pull the sled/driver system at a constant speed of 8.80 m/s where the coefficient of friction between the sled and the snow is 0.150? (the acceleration due to gravity is 9.81 m/s2.)
To find the force in the coupling between the dogs and the sled, use the equation F = ma where F is the force and m is the total mass. For the power supplied by each dog, calculate P = Fv where P is power, F is force, and v is velocity.
Explanation:The magnitude of the force in the coupling between the dogs and the sled: To calculate the force in the coupling, you can use the equation F = ma, where m is the total mass of the sled and rider, and a is the acceleration of the system. By using the force exerted by each dog and the acceleration calculated from that force, you can determine the force in the coupling. Power supplied by each dog: Power is defined as P = Fv, where F is the force applied and v is the velocity. Calculate the total force applied by all four dogs and the velocity of the sled, then use this information to determine the power supplied by each dog.
A coin dropped from the top of a precipice takes 5.00 s to hit the ground. How high is the precipice?
A) 49.1 m
B) 245 m
C) 123 m
D) 25.5 m
in a 4 kilometer race, a runner completes the first kilometer in 5.9 minutes, the second kilometer in 6.2 minutes, the third kilometer in 6.3 minutes, and the final kilometer in 6 minutes. the average speed of the runner for the race is approximately
Answer:
9.83 km/h
Explanation:
Given: in a 4 kilometer race, a runner completes the first kilometer in 5.9 minutes, the second kilometer in 6.2 minutes, the third kilometer in 6.3 minutes, and the final kilometer in 6 minutes.
To Find: the average speed of the runner for the race.
Solution:
In a 4 kilometer race,
time required to travel first kilometer = [tex]5.9[/tex] [tex]\text{minutes}[/tex]
time required to travel seoond kilometer = [tex]6.2[/tex] [tex]\text{minutes}[/tex]
time required to travel third kilometer = [tex]6.3[/tex] [tex]\text{minutes}[/tex]
time required to travel final kilometer = [tex]6[/tex] [tex]\text{minutes}[/tex]
we know that,
[tex]\text{Average speed}=\frac{\text{Total distance traveled}}{\text{Total time taken}}[/tex]
Total distance traveled = [tex]4[/tex] [tex]\text{kilometer}[/tex]
Total time taken = [tex](5.9+6.2+6.3+6)[/tex]
= [tex]24.4[/tex] [tex]\text{minutes}[/tex]
= [tex]\frac{24.4}{60}[/tex] [tex]\text{hours}[/tex]
putting values,
[tex]\text{Average speed}=\frac{4}{\frac{24.4}{60}}[/tex]
[tex]\text{Average speed}=\frac{4\times60}{24.4}[/tex]
=[tex]9.83[/tex] [tex]\text{km}/ \text{h}[/tex]
the average speed of the runner for the race is approximately [tex]9.83[/tex] [tex]\text{km}/ \text{h}[/tex]
Assume each tick mark represents 1 cm. Calculate the total displacement from 0 if an object moves 3 cm to the left, then 7 cm to the right, and then 6 cm to the left. The object moves cm to the left. What is the total distance the object travels? cm
The total displacement and total distance of the object that traveled should be -2cm and 16 cm.
Given that,
Each tick mark should be presented 1cm.If an object moves 3 cm to the left, then 7 cm to the right, and then 6 cm to the left.Here we assume a positive x-axis to the right-hand side.Based on the above information, the calculation is as follows:
The total displacement is
= 0 - 3 + 7 - 6
= -2 cm,
Thus, the object shifts 2 cm to the left-hand side.
Now
The total distance is
= 0 + 3 + 7 + 6
= 16 cm
Therefore we can conclude that the total displacement and total distance of the object that traveled should be -2cm and 16 cm.
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Answer:
The object moves ✔ 2 cm to the left.
What is the total distance the object travels? ✔ 16 cm.
Two cars pass each other traveling at the same speed. one car has a constant velocity of 15.0 m/s, east. the other car has a constant acceleration of 1.00 m/s , west. how much time will have elapsed until the cars are 164 m apart?
The formula for calculating the distance at constant velocity is:
d = v * t
d = 15 t
The formula for distance at constant acceleration is:
d = v0 t + 0.5 a t^2
d = 15 t + 0.5 t^2
So after a sum distance of 164 m:
15 t + (15 t + 0.5 t^2) = 164
30 t + 0.5 t^2 = 164
t^2 + 60 t = 328
(t + 30)^2 = 328 + 30^2
t + 30 = ± 35.04
t = -65.04, 5.04
Since time cannot be negative, so the two cars are 164 m apart after about 5 seconds
why is the scatterplot the most commonly used type of graph in science?
A coin completes 18 spins in 12 seconds. The centripetal acceleration of the edge of the coin is 2.2 m/s2. The radius of the coin is m.
Answer:
2.5 cm
Explanation:
Number of spins in 12 seconds = 18
Number of spins in 1 second = 18 / 12 = 1.5
Number of spins in one second is called frequency.
f = 1.5 rps
ac = 2.2 m/s^2
Let r be the radius of coin
Centripetal acceleration, ac = r x w^2
2.2 = r x ( 2 x 3.14 x 1.5) ^2
2.2 = r x 88.7364
r = 0.025 m = 2.5 cm
Answer: 0.025 m or 2.5m
Explanation:
The number of spins given in 12 seconds = 18
So the number of spins in 1 second will be
= 18 / 12 = 1.5rps
The above result is the frequency because it is the number of spins in one second
Let f be frequency
f = 1.5 rps
Using centripetal acceleration given
Ca = 2.2 m/s^2
m is the radius of the given coin
Using the formula
Centripetal acceleration, = m x w^2
Knowing that w = 2πf
2.2 = m x ( 2 x 3.14 x 1.5) ^2
2.2 = m x 88.7364
m = 0.025 m
What is the wavelength of an earthquake wave if it has a speed of 5 km/s and a frequency of 11 Hz?
The cold virus causes disease when it enters the _____ of the human body.
The cold virus causes disease when it enters the mucous membranes of the human body such as the nasal cavity.
The cold virus causes disease when it enters the mucous membranes of the human body, particularly the nasal cavity. The most common groups of cold viruses include rhinoviruses, coronaviruses, and adenoviruses. These viruses are transmitted through direct contact such as shaking hands, and droplet transmission which occurs when an infected person coughs or sneezes. The rhinoviruses in particular thrive in cooler temperatures found in the nasal passages, leading to symptoms such as runny nose, congestion, and sneezing.
Symptoms of a cold are a result of the body's inflammatory response to the viral infection. This response generates the typical signs of a cold, but the condition is usually self-limiting and resolves on its own within 1-2 weeks.
Borace drew a diagram to compare the processes of scientific investigation and technological design.
Which belongs in the area labeled W?
Conduct an experiment
Design a solution
Analyze the results
Build a prototype
Answer:
Conduct an experiment
Explanation:
Borace drew a diagram to compare the processes of scientific investigation and technological design, then the area labeled W belongs to the Conduct an experiment, therefore the correct answer is option A.
What are the stages of technological design?There are mainly five stages of the technological design
Identifying the issue that needs to be solved is the first step in every problem-solving process.
The second stage is to imagine; during this phase, a designer would generate several concepts and conduct research on potential creations. They must pick a handful of their greatest concepts and then narrow it down to the best.
The chosen product from the imaging stage is planned in the third stage.
Testing, evaluating, and modifying the product are the fourth stage.
Thus, If Borace drew a diagram to compare the processes of scientific investigation and technological design, then the area labeled W belongs to the Conduct an experiment, therefore the correct answer is option A.
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A statement that can be proven by observation or measurement is known as a(n): a. opinion b. value c. fact d. belief Please select the best answer from the choices provided
A statement that can be proven by observation or measurement is known as a fact , therefore the correct answer is option C
what is the scientific investigation?Scientific investigation is the process of looking for answers by doing extensive research and finding the answers through experimental results.
The scientific investigation very much relies on true experimental results that can be supported by evidence.
A scientific fact, also known as empirical evidence, is the outcome of persistent, meticulous observation or measurement by experimentation or another method. The development of scientific hypotheses depends on these.
Theories and facts are two distinct concepts. Facts, which can be observed and/or evaluated, and theories, which are scientists' justifications and assessments of the facts, are clearly distinguished in the scientific method.
Thus, a statement that can be proven by observation or measurement is known as a fact , therefore the correct answer is option C
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Compare the orderliness of the particles. In general, which state has the most orderly arrangement?
We have that the state with the orderly arrangement is
The Solid state
It is important to note that there are three states
Solid Liquid GaseousGenerally,The crystalline solid is the most well orderly arranged particle bond as it made up of a crystal lattice that has its particles well arranged.
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What are volume and density? How do they relate to each other?
______________________________
Density= It is the mass divided by the volume. Density is defined as the mass per unit volume.
Volume= the quantity of three-dimensional space enclosed by a closed surface, for example, the space that a substance (solid, liquid, gas, or plasma) or shape occupies or contains.
______________________________
Density expresses the proportional relationship between mass and volume of the substance. If the density of a particular substance is given in grams per milliliter, it indicates the number of grams present in 1 milliliter of that substance.
______________________________
during the first 50s a truck traveled at constant speed of 25m/s . Find the distance that it traveled
The truck, traveling at a constant speed of 25m/s for 50 seconds, covers a distance of 1250 meters.
Explanation:To calculate the distance the truck travels during the first 50 seconds at a constant speed, we can use the formula for distance based on speed and time:
Distance (d) = Speed (v) × Time (t)
Given that the truck's speed is 25m/s and the time is 50 seconds, we plug these values into the formula:
d = 25m/s × 50s
Upon multiplying, we find the main answer:
d = 1250 meters
Therefore, the truck traveled a total distance of 1250 meters in the first 50 seconds.
According to kinetic-molecular theory, if the temperature of a gas is raised from 100 °c to 200 °c, the average kinetic energy of the gas will ________.
Actually the Kinetic Energy, which is also known as the energy of motion is directly proportional to temperature. So the higher the temperature is, the faster the gas particles move so they have possess more kinetic energy.
This temperature is in absolute units so we convert to Kelvin:
200 C = 473.15 K
100 C = 373.15 K
So the amount increase is:
473.15 / 373.15 = 1.268
It will increase by a factor of 1.268 or 126.8%
The average kinetic energy of the gas will increase by a factor of 1.27
[tex]\texttt{ }[/tex]
Further explanationThe Ideal Gas Law that needs to be recalled is:
[tex]\large {\boxed {PV = nRT} }[/tex]
P = Pressure (Pa)
V = Volume (m³)
n = number of moles (moles)
R = Gas Constant (8.314 J/mol K)
T = Absolute Temperature (K)
Let us now tackle the problem !
[tex]\texttt{ }[/tex]
Given:
initial temperature of the gas = T₁ = 100°C = 373 K
final temperature of the gas = T₂ = 200°C = 473 K
Asked:
ratio of average kinetic energy of the gas = Ek₁ : Ek₂
Solution:
[tex]Ek_1 : Ek_2 = \frac{3}{2}kT_1 : \frac{3}{2}kT_2[/tex]
[tex]Ek_1 : Ek_2 = T_1 : T_2[/tex]
[tex]Ek_1 : Ek_2 = 373 : 473[/tex]
[tex]Ek_2 = \frac{473}{373} Ek_1[/tex]
[tex]Ek_2 \approx 1.27 \times Ek_1[/tex]
[tex]\texttt{ }[/tex]
Conclusion:The average kinetic energy of the gas will increase by a factor of 1.27 if the temperature of a gas is raised from 100°C to 200°C.
[tex]\texttt{ }[/tex]
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Answer detailsGrade: High School
Subject: Physics
Chapter: Pressure
compare the bouyant force of water and the weight of a piece of wood that floats on the water
All of the following are properties of metals except: Question 1 options: malleable ductile luster brittle
Identify the total number of protons and neutrons in the nucleus of the most common isotope of manganese
Is the change in kinetic energy of your ball greater than, less than, or equal to the change in kinetic energy of your friend's ball?
A force of 250 N is applied to an object that accelerates at a rate of 10m/sec2. What is the mass of the object?
A particle of mass m=5.00 kilograms is at rest at t=0.00 seconds. a varying force f(t)=6.00t2−4.00t+3.00 is acting on the particle between t=0.00 seconds and t=5.00 seconds. find the speed v of the particle at t=5.00 seconds. express your answer in meters per second to three significant figures.
The speed of the particle at [tex]t = 5\,{\text{s}}[/tex] is [tex]\fbox{43\,{\text{m/s}}}[/tex].
Further explanation:
Applied force is directly proportional to the mass of the body and the acceleration of the body.
Given:
The function for force is [tex]F\left( t \right) = 6{t^2} - 4t + 3[/tex].
The limit of time is [tex]t = 0\,{\text{s}}[/tex] to [tex]t = 5\,{\text{s}}[/tex].
The mass of the particle is [tex]5\,{\text{Kg}}[/tex].
Concept used:
The rate of change of displacement of a body in unit time is called speed of the body. It is a scalar quantity.
Newton’s second law of motion states that the rate of change of momentum is equal to the applied force.
The expression for the Newton’s second law is given as.
[tex]F=ma[/tex]
Rearrange the expression for the acceleration of the body.
[tex]a=\dfrac{F}{m}[/tex] …… (1)
Here, a is the acceleration of the body, F is the force applied and m is the mass of the body.
The rate of change of speed of a body in unit time is called acceleration of the body.
The expression for the acceleration is given as.
[tex]a=\dfrac{{dv}}{{dt}}[/tex]
Substitute [tex]\dfrac{{dv}}{{dt}}[/tex] for [tex]a[/tex] in equation (1).
[tex]\dfrac{{dv}}{{dt}} = \dfrac{F}{m}[/tex]
On integrating the above expression we get.
[tex]v = \dfrac{1}{m}\int\limits_0^5 {Fdt}[/tex] …… (2)
Substitute [tex]6{t^2} - 4t + 3[/tex] for[tex]F\left(t\right)[/tex] and [tex]5\,{\text{Kg}}[/tex] for m in equation (2).
[tex]\begin{aligned} v&=\frac{1}{{\left( {5\,{\text{Kg}}} \right)}}\int\limits_0^5 {\left( {6{t^2} - 4t + 3} \right)dt}\\&=\frac{1}{{\left( {5\,{\text{Kg}}}\right)}}\left|{3{t^3}-2{t^2}+ 3t}\right|_0^5\\&=\frac{{215}}{{5\,}}\,{\text{m/s}}\\&=43\,{\text{m/s}}\\\end{aligned}[/tex]
Thus, the speed of the particle is [tex]\fbox{43\,{\text{m/s}}}[/tex].
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Answer Details:
Grade: College
Subject: Physics
Chapter: Kinematics
Keywords:
Acceleration, force, weight, mass, motion, impact, nail, hammer, acceleration, duration of impact, Newton’s laws, speed, rate of change, time , 43m/s, 5Kg.
An electric field is established by applying a potential difference to the plates. it is found that a field of strength e0 will cause the droplet to be suspended motionless. write an expression for the droplet's charge q. let g be the acceleration due to gravity.
Final answer:
When a droplet is motionless in an electric field, it means the electrical force exactly balances gravity. Coulomb's law defines the electrical force as proportional to charge [tex](\( q \))[/tex] and the field strength [tex](\( E_0 \))[/tex]. Meanwhile, gravity exerts a force[tex]\( mg \)[/tex], where [tex]\( m \)[/tex] is the droplet's mass and [tex]\( g \)[/tex] is gravity's acceleration. Equilibrium occurs when these forces match:
[tex]\[ qE_0 = mg \][/tex]
Rearranging, we find the droplet's charge [tex]\( q \):[/tex]
[tex]\[ q = \frac{mg}{E_0} \][/tex]
This expression signifies the charge required for equilibrium in the given electric field.
Explanation:
To find the expression for the droplet's charge [tex](\( q \)),[/tex] we can use the equilibrium condition where the electric force [tex](\( F_{\text{electric}} \))[/tex] due to the electric field [tex](\( E_0 \))[/tex]balances the gravitational force [tex](\( F_{\text{gravity}} \))[/tex]acting on the droplet.
The electric force [tex](\( F_{\text{electric}} \))[/tex] exerted on the droplet with charge [tex]\( q \) i[/tex]n an electric field [tex]\( E_0 \)[/tex] is given by Coulomb's law:
[tex]\[ F_{\text{electric}} = qE_0 \][/tex]
The gravitational force [tex](\( F_{\text{gravity}} \))[/tex] acting on the droplet with mass [tex]\( m \)[/tex] in a gravitational field [tex]\( g \)[/tex] is given by:
[tex]\[ F_{\text{gravity}} = mg \][/tex]
At equilibrium, these forces balance each other:
[tex]\[ qE_0 = mg \][/tex]
Solving for [tex]\( q \):[/tex]
[tex]\[ q = \frac{mg}{E_0} \][/tex]
So, the expression for the droplet's charge [tex]\( q \)[/tex] is:
[tex]\[ q = \frac{mg}{E_0} \][/tex]
Two masses m1 = 5.40 kg and m2 which has a mass 80.0% that of m1, are attached to a cord of negligible mass which passes over a frictionless pulley also of negligible mass. If m1 and m2 start from rest, after they have each traveled a distance h = 2.00 m, use energy content to determine the following.
(a) speed v of the masses
To determine the speed of the masses after traveling a distance of 2.00 m, we can use the principle of conservation of energy.
Explanation:To determine the speed of the masses after traveling a distance of 2.00 m, we can use the principle of conservation of energy. The initial potential energy of the system is equal to the final kinetic energy. The potential energy is given by m1gh, where g is the acceleration due to gravity and h is the distance traveled. The kinetic energy is given by (1/2)m1v^2 + (1/2)m2v^2, where v is the speed of the masses.
Given that m2 has a mass of 80.0% of m1, m2 = 0.80 * m1. Plugging this information into the equation and solving for v, we get:
v = √(2gh / (m1 + m2))
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A roller coaster car rapidly picks up speed as it rollsdown a slope. As it starts down the slope its speed is 4m/s. But 3 seconds later, at the bottom of the slope, its speed is 22m/s. What is its average acceleration?
With your hand parallel to the floor and your palm upright, you raise a 3-kg book upward with an acceleration of 2 m/s2. what is the magnitude of force that your hand exerts on the book while it is accelerating?
Answer:
35 N
Explanation:
We are using Newton's law of motion.
Here is what we know:
(T-w)= ma
w = 3 kg (we will change to Newtons in a second)
a = 2m/s^2
rearrange equation to solve for T (tension)
T = ma+w
all we need is mass
Now to get the correct mass we need to divide its weight by the gravitational field strength(in our case it is just gravity) but first we want our weight of 3kg to be in Newtons.
1 kg = 9.81 N
w = (3)(9.81) = 29.4N
Now that our weight is 29.4N we need to divide that by gravity.
m = [tex]\frac{29.4}{9.8}[/tex]
Now that we have mass we can plug in our numbers
[tex](\frac{29.4}{9.8}*2)+29.4 = 35.4N[/tex]
Plugging that into our calculator gives us the answer 35.4 or 35 N
(feel free to correct me if my reasonings for any of this stuff is incorrect)
The magnitude of force that your hand exerted on the book while it accelerates is 35.4 N.
The given parameters;
mass of the book, m = 3 kgacceleration of the book, a = 2 m/s²The magnitude of force that your hand exerted on the book while it accelerates is the tension on your hand.
The tension on your hand while the book accelerates is calculated using Newton's second law of motion;
F = ma
T = ma + w
T = ma + mg
T = m(a + g)
T = 3(2 + 9.8)
T = 35.4 N
Thus, the magnitude of force that your hand exerted on the book while it accelerates is 35.4 N.
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What was his average swimming speed during the second half of the race if he tied the record, which was at an average speed of 2.05 m/s?
I believe this question has additional detail which stated that during the 1st half, his speed was 2.01 m/s. From this we can calculate his speed during the second half, v2, using the formula:
v_ave = (v1 + v2) / 2
2.05 m/s = (2.01 m/s + v2) / 2
v2 = 2.09 m/s
A brick is dropped from rest from the top of a building through air (air resistance is present) to the ground below. how does the brick's kinetic energy just before reaching the ground compare with the gravitational potential energy at the top of the building? set zero height at the ground level. the comparison cannot be made since the information of air resistance is not given. kinetic energy just before reaching the ground < gravitational potential energy at the top of the building kinetic energy just before reaching the ground = gravitational potential energy at the top of the building kinetic energy just before reaching the ground > gravitational potential energy at the top of the building
The correct answer is kinetic energy just before reaching the
ground < gravitational potential energy at the top of the building.
We have,
In the absence of air resistance, when the brick is dropped from rest, it will convert all its initial potential energy (due to its height above the ground) into kinetic energy as it accelerates downward.
However, with air resistance present, some of the initial potential energy is converted into other forms of energy, such as heat, due to the work done by air resistance.
As a result, the brick's kinetic energy just before reaching the ground will be less than the gravitational potential energy it had at the top of the building.
Thus,
kinetic energy just before reaching the ground < gravitational potential energy at the top of the building.
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The kinetic energy of the brick just before reaching the ground is greater than the gravitational potential energy at the top of the building.
Explanation:The kinetic energy of the brick just before reaching the ground is greater than the gravitational potential energy at the top of the building.
When the brick is dropped from rest, it starts accelerating due to the force of gravity. As it falls, the brick's gravitational potential energy is converted into kinetic energy, increasing its speed. The brick's kinetic energy just before reaching the ground is at its maximum, while its gravitational potential energy at the top of the building is at its minimum. Therefore, the comparison is such that the kinetic energy just before reaching the ground > gravitational potential energy at the top of the building.
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