The earth has a net electric charge that causes a field at points near its surface equal to 150 N/C and directed in toward the center of the earth. (a) What magnitude and sign of charge would a 60-kg human have to acquire to overcome his or her weight by the force exerted by the earth’s electric field? (b) What would be the force of repulsion between two people each with the charge calculated in part (a) and separated by a distance of 100 m? Is use of the earth’s electric field a feasible means of flight? Why or why not?
Answers
Answer:
a) The magnitude of the electric charge that a 60-kg human must have to overcome weight is 3.923 coulombs and its sign is negative.
b) The force of repulsion between two people is \(13.851\times 10^{6}\) newtons. The use of the earth's electric field a feasible means of flight is not feasible since electric force of repulsion would destroy human body before taking advantage of any possible flight skill.
Explanation:
a) From Second Newton's Law, we form this equation of equilibrium:
\(\Sigma F = F_{E}-W = 0\) (Eq. 1)
Where:
\(F_{E}\) - Electrostatic force exerted on human, measured in Newton.
\(W\) - Weight of the human, measured in Newton.
If we consider that human can be represented as a particle and make use of definitions of electric field and weight, the previous equation is expanded and electric charge is cleared afterwards:
\(q\cdot E-m\cdot g = 0\)
\(q = \frac{m\cdot g}{E}\) (Eq. 2)
\(E\) - Electric field, measured in Newtons per Coloumb.
\(m\) - Mass, measured in kilograms.
\(g\) - Gravity acceleration, measured in meters per square second.
\(q\) - Electric charge, measured in Coulomb.
As electric field of the Earth is directed in toward the center of the planet, that is, in the same direction of gravity, electric field must be a negative value. If we know that \(m = 60\,kg\), \(g = 9.807\,\frac{m}{s^{2}}\) and \(E = -150\,\frac{N}{C}\), the charge that a 60-kg human must have to overcome weight is:
\(q = \frac{(60\,kg)\cdot \left(9.807\,\frac{m}{s^{2}} \right)}{-150\,\frac{N}{C} }\)
\(q = -3.923\,C\)
The magnitude of the electric charge that a 60-kg human must have to overcome weight is 3.923 coulombs and its sign is negative.
b) The electric force of repulsion between two people with the same charge calculated in part (a) is determined by Coulomb's Law, whose definition we proceed to use:
\(F = \kappa \cdot \frac{q^{2}}{r^{2}}\) (Eq. 3)
Where:
\(\kappa\) - Electrostatic constant, measured in Newton-square meter per square Coulomb.
\(q\) - Electric charge, measured in Coulomb.
\(r\) - Distance between two people, measured in meters.
If we know that \(\kappa = 9\times 10^{9}\,\frac{N\cdot m^{2}}{C^{2}}\), \(q = -3.923\,C\) and \(r = 100\,m\), then the force of repulsion between two people is:
\(F = \left(9\times 10^{9}\,\frac{N\cdot m^{2}}{C^{2}} \right)\cdot \left[\frac{(-3.923\,C)^{2}}{(100\,m)^{2}} \right]\)
\(F = 13.851\times 10^{6}\,N\)
The force of repulsion between two people is \(13.851\times 10^{6}\) newtons. The use of the earth's electric field a feasible means of flight is not feasible since electric force of repulsion would destroy human body before taking advantage of any possible flight skill.
Related Questions
If a person walks 1 km north, 5 km west, 3 km south and 7 km east, find the resultant displacement vecto
Answers
If a person walks 1km north, 5 km West, 3km south, and 7km east, then the resultant displacement vector would be 2.82 km toward the south east direction
What is displacement?
When an object moves in connection to a reference frame, such as when a passenger travels to the back of an airliner or a professor walks to the right in relation to a whiteboard, its position changes. This movement in position is described as displacement.
as stated in the issue If a person goes one kilometre north, five kilometres west, three kilometres south, and seven kilometres east,
The resulting displacement vector, as we know, is the shortest feasible distance between the beginning and ending points
In the horizontal direction, the outcome is
7-5 pointing east
2 kilometres to the eas
In the vertical direction, the outcome is
3–1 km to the south
2 kilometres to the south
\($\begin{aligned} \text { Resultant displacement } &=\sqrt{ }\left(2^{2}+2^{2}\right) \\ &=2 \cdot \sqrt{2} \\ &=2.82 \end{aligned}$\)
As a result, the resulting displacement vector is 2.82 kilometres to the southeast.
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Two equal and opposite charges are placed 40mm apart,if the force between them is found to be 0.5N Calculate the magnitude of the charge
Answers
F = k * (q1 * q2) / r^2
where k is Coulomb's constant (9 x 10^9 N m^2 C^-2).
In this problem, we have two equal and opposite charges, so we can assume that q1 = -q2 = q. The distance between them is 40 mm, which is 0.04 m. We are given that the force between them is 0.5 N. Therefore, we can set up an equation:
0.5 N = k * (q * q) / (0.04 m)^2
Simplifying and solving for q:
q^2 = (0.5 N * (0.04 m)^2) / k
q^2 = (0.5 N * (0.04 m)^2) / (9 x 10^9 N m^2 C^-2)
q^2 = 8.88 x 10^-12 C^2
q = sqrt(8.88 x 10^-12 C^2)
q = 2.98 x 10^-6 C
Therefore, the magnitude of each charge is 2.98 x 10^-6 C.
a plane wall is 250mm thick and it's wall area is 4.5m^2. if the thermal conductivity is 9.35w/m°c and surface temperature are steady at 150°c and 40°c. calculate the heat flow across the plane wall and the temperature gradient in the flow direction
Answers
The temperature gradient in the flow of direction is 294525 W.
What is Temperature gradient?A temperature gradient is the gradual variance in temperature with distance. The slope of the gradient is consistent within a material. A gradient is established anytime two materials at different temperatures are in physical contact with each other.
Q= T/( L/ KA)
Q= ( 1500 − 450) / 0.15 / 9.35v * 4.35)
= 294525 W
Units of measure of temperature gradients are degrees per unit distance, such as °F per inch or °C per meter.
Many temperature gradients exist naturally, while others are created. The largest temperature gradient on Earth is the Earth itself. Q= T/Ka.
Therefore, The temperature gradient in the flow of direction is 294525 W.
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A dryer uses electrical energy to spin a drum and produce heat. It uses 220 V of an electric charge and 50 A of electric current. What is the dryer power?
Answers
The power used by the dryer to spin the drum and produce heat is 11000 Watts.
What is the power of the dryer?Power is simply the quantity of energy transferred per unit time.
This is expressed as;
P = v × I
Where v is voltage and I is current.
Given that;
Voltage v = 220VCurrent I = 50APower P = ?Plug the given values into the above formula and solve for P.
P = v × I
P = 220V × 50A
P = 11000 Watts
Therefore, the power used by the dry is 11000 Watts.
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1)What is the pressure at point D in kPa ?
2)Temperature at point D
3)What is the net work done on the gas as it is taken through four cycles?
4)What is the internal energy of the gas when it is at point A?
5)What is the total change in internal energy of this gas during four complete cycles?
Answers
The answer is 1) The pressure at point D is 80 kPa. 2) The temperature at point D is 800 K. 3) The net work done on the gas over four cycles is zero. 4) The internal energy of the gas at point A is 100 J. 5) The total change in internal energy during four complete cycles is zero.
The total change in internal energy of this gas during four complete cycles is zero. The given diagram represents the Carnot cycle involving four stages. The four stages of the Carnot cycle are reversible and follow an ideal gas that is placed in a cylinder with a movable piston.Let's solve each question asked one by one.1) From the graph, it can be observed that the pressure at point D is 0.08 M Pa, which is equal to 80 kPa. Hence, the pressure at point D in kPa is 80 kPa.2) Temperature at point D The isotherm at point D is about 800 K. Hence, the temperature at point D is 800 K.3) The net work done on the gas as it is taken through four cycles is zero because the Carnot cycle is a cycle that has four stages. In each cycle, the net work done is the area enclosed by the cycle. Therefore, for a complete cycle, the net work done is zero because the area enclosed is a loop.4) The internal energy of the gas when it is at point A is 100 J because the internal energy of the gas is directly proportional to the temperature and volume. Here, at point A, the temperature is 500 K, and the volume is 2 m³, so the internal energy of the gas when it is at point A is 100 J.5) The Carnot cycle is a reversible cycle that is used to determine the efficiency of heat engines. It is a closed cycle that does not involve any net energy exchange with the surroundings. Therefore, the total change in internal energy of this gas during four complete cycles is zero since the initial and final states are the same. Hence, the total change in internal energy of this gas during four complete cycles is zero.For more questions on the Carnot cycle, click on:
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true or false
Almost all of Earth's atmosphere is created through the process of photosynthesis.
Answers
Answer:
true
Explanation:
I believe the answer i chose because the earths atmosphere is mostly made up of different things that causes the earth to interact with human life and also interacts with what's in the atmosphere like energy oxygen carbon dioxide and all the stuff like that i hope its right.
In a 'keep-fit' exercise, a student of mass 45 kg steps 40 times on and off a box of height 0.50 m. How much work does the student do to raise her body each time she steps on the box
Answers
Answer:Calculate the work done using:
work done (in joules) = force (in newtons) x distance moved (in metres)
To practice calculations involving force, distance and work done.
Explanation: I hope this helps srry if I'm wrong
a 9000 kg car moving at 8 m/s due east collides with a 12000 kg suv moving due west at 7m/s. after collision, the 9000 kg moves due west at 6 m/s. calculate the momentum of the suv. determine the speed of the suv.
Answers
Given,
The mass of the car, m₁=9000 kg
The velocity of the car before collision, u₁=8 m/s
The mass of the SUV, m₂=12000 kg
The velocity of the SUV before the collision, u₂=-7 m/s
The velocity of the car after the collision, v₁=-6 m/s
Here we consider that the east is the positive direction and the west is the negative direction, hence all the westward velocities are negative.
The momentum of an object is the product of its velocity and mass.
From the law of conservation of momentum, the total momentum of the car and the SUV before the collision is equal to the total momentum of the car and the SUV after the collision.
Thus,
\(\begin{gathered} p_{1i}+p_{2i}=p_{1f}+p_{2f} \\ m_1u_1+m_2u_2=m_1v_1+p_{2f} \end{gathered}\)Where:
• p₁i and p₁f are the momenta of the car before and after the collision respectively.
,• p₂i and p₂f are the momenta of the suv before and after the collision respectively.
On substituting the known values,
\(\begin{gathered} (9000\times8)+(12000\times-7)=(9000\times-6)+p_{2f} \\ \Rightarrow p_{2f}=(9000\times8)+(12000\times-7)-(9000\times-6) \\ =42000\text{ kg}\cdot\text{m/s} \end{gathered}\)Therefore the momentum of the SUV after the collision is 42000 kg·m/s
The velocity of the SUV after the collision is given by,
\(v_2=\frac{p_{2f}}{m_2}\)On substituting the known values,
\(\begin{gathered} v_2=\frac{42000}{12000} \\ =3.5\text{ m/s} \end{gathered}\)Thus the speed of the SUV after the collision is 3.5 m/s
what is prefixe name of 1.5×10⁴
Answers
Answer:
10000
Explanation:
10 to the 5th power
Hhjhjjjjhhhhhhhffjmgr??
Answers
Answer:
Hi
Explanation:
Amino acids are organic compounds that contain amino and carboxylate functional groups, along with a side chain specific to each amino acid.
The source of sound moves away from the listener.The listener has the impression that the source is lower in pitch. Why?
Answers
When the source is moving away from the observer the velocity of the source is added to the speed of light. This increases the value of the denominator, decreasing the value of the observed frequency. Frequency corresponds to pitch or tone; a lower observed frequency will result in a lower observed pitch.
A book that weighs 5 newtons is sitting on a table 1.5 meters above the floor. How much gravitational potential energy does the book have?6.5 joules
4.5 joules
7.5 joules
3.33 joules
Answers
Answer:7.5J
Explanation:7.5
J
Explanation:
P
E
=
m
g
h
Since
F
=
m
g
in this case
P
E
=
F
h
P
E
=
5
N
⋅
1.5
m
=
7.5
An object has a mass of 450g. What is the gravitational force of the object by earth?
Answers
Answer:
4.41N or 4.5N (check explanation)
Explanation:
450g = 0.45kg
F = ma
Using 10m/s² = 10(0.45) = 4.5N
Using 9.8m/s² = 9.8(0.45) = 4.41N
Which interaction does not take place due to field forces?
A.
interaction between protons and electrons
B.
interaction between a ball in flight and the earth below it
C.
interaction between Mars and the Sun
D.
interaction between a pen and paper while you write
Answers
The interaction that does not take place due to field forces is the interaction between a pen and paper while you write.
What is the gravity law?
Gravity law is a well-established scientific theory that states objects can attract each other according to their masses.
This theory (gravity law) was developed by Sir Isaac Newton to explain the movement of objects.
In conclusion, the interaction that does not take place due to field forces is the interaction between a pen and paper while you write.
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which is an example of a scientist using a mathematical model to describe the weather?
A. The scientist finds an equation that predicts how long a rainstorm will last.
B. The scientist says that a lightning bolt is like a long snake.
C. The scientist uses cotton balls to represent clouds, and grass to represent the ground.
D. The scientist thinks of a cloud as a giant ball of cotton candy.
(its A)
Answers
Answer:
The scientist finds an equation that predicts how long the rainstrom will last.
Explanation:
I just answered it :)
can someone give me a 5 day fitness plan with all the reps and sets for 3 only and 4 exercises a day
Answers
Answer:
Classic 5 Day Split
Day 1 – Chest
Day 2 – Legs
Day 3 – Rest
Day 4 – Back
Day 5 – Arms
Day 6 – Shoulders
Day 7 – Rest
Upper Lower Push Pull Legs
Day 1 – Upper
Day 2 – Lower
Day 3 – Rest
Day 4 – Push
Day 5 – Pull
Day 6 – Legs
Day 7 – Rest
5 Day Split Variation
Day 1 – Chest
Day 2 – Legs & Shoulders
Day 3 – Back
Day 4 – Biceps & Triceps
Day 5 – Core & Cardio
Day 6 – Rest
Day 7 – Rest
Explanation:
A 4.9-m wide swimming pool is filled to the top. The bottom of the pool becomes completely shaded in the afternoon when the sun is 25 degrees above the horizon. How deep is the pool?
Answers
Answer:
Explanation:
We can solve this problem using trigonometry. Let's draw a diagram:
|\
| \
| \ <- Sun rays
| \
| \
| \
| \
---------
Pool
The angle between the sun rays and the horizontal line is 90 - 25 = 65 degrees. Let's call the depth of the pool "d". We want to find the value of "d" that makes the bottom of the pool completely shaded.
We can see that the triangle formed by the sun rays, the top edge of the pool, and the bottom edge of the shaded area is a right triangle. The angle between the sun rays and the top edge of the pool is also 65 degrees, because the top edge is parallel to the ground.
Using trigonometry, we can write:
tan(65 degrees) = d / 4.9 m
Solving for "d", we get:
d = 4.9 m * tan(65 degrees)
Using a calculator, we find:
d ≈ 13.7 m
Therefore, the pool is approximately 13.7 meters deep.
Using the equation for Impulse, can you explain the following:
Why are car steering rods designed to collapse?
Why are highway guard rails designed to crumple up on impact?
Why are traffic safety barrels filled with water or sand?
Answers
Answer :
The equation of impact is shown the impulse.
Explanation :
Given that,
The following statements are,
(I). Why are car steering rods designed to collapse?
(II). Why are highway guard rails designed to crumple upon impact?
(III). Why are traffic safety barrels filled with water or sand?
We know that,
The equation of impact is shown the impulse.
Impulse :
Impulse is equal to the change in momentum.
In mathematically,
\(\Delta p=F\Delta t\)
Where, \(\Delta p\) = change in momentum
F = force
\(\Delta t\) = change in time
We can be minimized of force of impact by maximizing the time of impact.
We can explain the following statements,
(I). Car steering rods designed to collapse for increases the time of impact, decreases the force of impact and reduce the damage caused
(II). Highway guard rails designed to crumple upon impact for increases the time of impact, decreases the force of impact and reduce the damage caused
(III). Traffic safety barrels filled with water or sand because they are increased the time impact.
Hence, The equation of impact is shown the impulse.
What are political obstacles keeping wind turbine from being used?
Answers
Explanation:
Turbines might cause noise and aesthetic pollution.
Although wind power plants have relatively little impact on the environment compared to conventional power plants, concern exists over the noise produced by the turbine blades and visual impacts to the landscape.
The inflexibility, variability, and relative unpredictability of wind power as a means for electricity production, are the most obvious barriers to an easy integration and widespread application of wind power." Thus, the uncertainty of the wind requires a system that is always available to replace all the electrical output created by the wind turbine system. In other words, it is too expensive to have wind turbines lying around that don't do anything.
Which point on the standing wave is a node?
A.A
B.B
C.C
D.D
Answers
Point B on the standing wave is referred to as a node. The correct option is B.
In a standing wave, a node refers to a point or region of minimal or zero amplitude. It is a point where the displacement of the wave is always zero, and it remains stationary as the wave oscillates. At a node, the particles or elements that make up the medium through which the wave is propagating do not experience any displacement from their equilibrium positions.
Nodes occur due to destructive interference between two waves of equal frequency and amplitude traveling in opposite directions. The superposition of these waves results in the formation of a standing wave pattern, characterized by nodes and antinodes.
Nodes are important features of standing waves and have several properties:
Fixed position: Nodes maintain a fixed location within the standing wave pattern and do not move as the wave oscillates.
Zero displacements: At nodes, the amplitude of the wave is zero, and there is no displacement of the medium particles or elements.
Energy concentration: Nodes are regions of low energy in a standing wave. The energy of the wave is primarily concentrated in the regions between the nodes, known as antinodes.
Separation distance: The distance between adjacent nodes in a standing wave is equal to half the wavelength of the wave.
Therefore, The correct answer is option B.
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Place a small object on the number line below at the position marked zero. Draw a circle around the object. Mark the center of this circle with the symbol for “initial position”. Move the object 5.0cm to the right and stop. Label this circle with the correct symbol for “final position.”

(A) What was the initial position of the object?
(B) What is the final position of the object?
(C) What is the distance traveled by the object?
(D) What is the displacement of the object?
(E) Of the three underlined quantities, which are numerically equal?
Answers
This interaction is not possible in nature because it violates a conservation law. Which quantity is not conserved?
p+ e-+ --> π+n+ve
Answers
Answer:
its D i just did it on the app
5. Sandor fills a bucket with water and whirls it in a vertical circle to demonstrate that the
water will not spill from the bucket at the top of the loop. If the length of the rope from his
hand to the centre of the bucket is 1.24 m, what is the minimum tension in the rope (at the
top of the swing)? How slow can he swing the bucket? Explain your answer.
Answers
Given that,
radius = 1.24 m
According to question,
The rope cannot push outwards. It must always have some slight tension or the bucket will fall.
We need to calculate the tension in the rope
At the top the force of gravity is
\(F=mg\)
The force needed to move the bucket in a circle is centripetal force.
So, if mg is ever greater than centripetal force then the bucket and the contents will start to fall.
The rope have a tension of less than zero.
We need to calculate the velocity of swing bucket
Using centripetal force
\(F=\dfrac{mv^2}{r}\)
\(mg=\dfrac{mv^2}{r}\)
\(g=\dfrac{v^2}{r}\)
\(v^2=gr\)
\(v=\sqrt{gr}\)
Put the value into the formula
\(v=\sqrt{9.8\times1.24}\)
\(v=3.49\ m/s\)
Hence, The minimum tension in the rope is less than zero .
The bucket swings with the velocity of 3.49 m/s.
What are the two fundamental ways energy and momentum are moved from one place to another?
Answers
The two fundamental ways energy and momentum are moved from one
place to another are through the mass and velocity.
The formula for momentum is mass multiplied with velocity.
Momentum= mass × velocity
The two factors in which momentum and energy is moved from one place to
another is however through how much and how fast the object is moving
which validates the answer.
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A surface is bombarded by particles, each of mass small 'm', which have velocity
normal to the surface. On average, n particles strike unit area of the surface each second
and rebound elastically. What is the pressure on the surface?
A. nmv
B. 2nmv
C. nmv²
D. 1/2nmv²
Answers
Answer:
B. 2nmv
Explanation:
Pressure is force over area.
P = F / A
Force is mass times acceleration.
F = ma
Acceleration is change in velocity over change in time.
a = Δv / Δt
Therefore:
F = m Δv / Δt
P = m Δv / (A Δt)
The total mass is nm.
The change in velocity is Δv = v − (-v) = 2v.
A = 1 and Δt = 1.
Plugging in:
P = (nm) (2v) / (1 × 1)
P = 2nmv
What is the potential energy of a 12 kg box on a 5 m high shelf?
Answers
Answer:6
Explanation:$’n
Question:why do some liquids flow really fast and other flow really slow?does temperature affect the rate of flow?
If the thickness of the liquid affects its flow rate
Then————
Figure out the then part by the question
Answers
Answer:
Some liquids flow really fast and some flow really slow.
Explanation:
This is because of a liquids viscosity , If the liquids viscosity is high it will flow really slow like syrup. But if it has high viscosity it will flow really fast much like water.
Hope this helped!! :)
Discuss the multiple ways in which intellect and aging are related
Answers
Factors such as Cognitive function, Wisdom & experience,genetics, lifestyle choices, education, etc play a role in determining how aging affects intellect.
Intellect and aging are related in multiple ways. Here are some key aspects to consider:
Cognitive Function: As individuals age, there is a general decline in cognitive function, including memory, processing speed, and problem-solving abilities. This decline can affect intellectual performance, such as reasoning and decision-making skills.
Wisdom and Experience: Despite the cognitive decline associated with aging, older adults often possess a wealth of knowledge and experience accumulated over their lifetime. This experiential wisdom can compensate for certain cognitive deficits and contribute to intellectual growth.
Lifelong Learning: Intellectual engagement and learning opportunities play a vital role in maintaining cognitive abilities as one ages. Continuing to challenge the mind through activities like reading, puzzles, learning new skills, and pursuing education can help slow down cognitive decline and promote intellectual well-being.
Expertise and Specialization: With age comes the opportunity for individuals to specialize in certain fields or develop expertise in specific areas. This specialization can lead to a deeper understanding and enhanced intellectual abilities within those particular domains.
Emotional Intelligence: Aging is often associated with increased emotional intelligence. Older adults tend to have a better understanding of their emotions and the emotions of others, which can positively impact their intellectual interactions and decision-making processes.
Neuroplasticity: Although aging is typically associated with a decline in cognitive abilities, research has shown that the brain remains capable of plasticity throughout life. This means that individuals can continue to learn, adapt, and form new neural connections, potentially offsetting some of the cognitive decline associated with aging.
Health Factors: Physical and mental health can significantly influence intellectual functioning in older adults. Chronic health conditions, such as cardiovascular disease, diabetes, or neurodegenerative disorders, can impact cognitive abilities. Conversely, maintaining good physical and mental health through regular exercise, a balanced diet, social engagement, and managing stress can support intellectual well-being.
It's important to note that the relationship between intellect and aging is complex and varies between individuals. While some may experience significant cognitive decline, others may maintain their intellectual abilities well into old age. Factors such as genetics, lifestyle choices, education, and overall cognitive reserve also play a role in determining how aging affects intellect.
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A 80kg stone falls from the top of the 360 meter cliff. Neglecting friction, how fast will the stone be moving just before it hits the ground?
Answers
The stone will be moving at a speed of approximately 84.4 meters per second just before it hits the ground, neglecting friction.
To find how fast will the stone be moving just before it hits the ground?This problem can be solved using the laws of kinematics and conservation of energy. The potential energy of the stone at the top of the cliff is converted to kinetic energy as it falls. We can equate the potential energy at the top of the cliff to the kinetic energy just before hitting the ground.
Potential energy = mgh,
Where
m is the mass of the stone g is the acceleration due to gravity (9.8 m/s^2) h is the height of the cliff (360 meters)Kinetic energy = (1/2)mv^2,
Where
v is the velocity of the stone just before hitting the ground.Equating these two expressions and solving for v, we get:
mgh = (1/2)mv^2
v^2 = 2gh
v = sqrt(2gh)
Plugging in the given values, we get:
v = sqrt(2 x 9.8 m/s^2 x 360 m) = 84.4 m/s
Therefore, the stone will be moving at a speed of approximately 84.4 meters per second just before it hits the ground, neglecting friction.
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Suppose a car is traveling at 18.6 m/s, and the driver sees a traffic light turn red. After 0.500 s has elapsed (the reaction time), the driver applies the brakes, and the car decelerates at 4.00 m/s2. What is the stopping distance of the car, as measured from the point where the driver first notices the red light
Answers
Answer:
s = 52.545 m
Explanation:
First, we calculate the distance covered during the 0.5 s when the driver notices the light and applies the brake.
\(s_{1} = vt\\\)
where,
s₁ = distance covered between noticing light and applying brake = ?
v = speed = 18.6 m/s
t = time = 0.5 s
Therefore,
\(s_{1} = (18.6\ m/s)(0.5\ s)\\s_{1} = 9.3\ m\\\)
Now, we calculate the distance for the car to stop after the application of brakes. For that we use 3rd equation of motion:
\(2as_{2} = V_{f}^{2} - V_{i}^{2}\\\\\)
where,
s₂ = distance covered after applying brake = ?
a = deceleration = - 4 m/s²
Vf = final speed = 0 m/s
Vi = initial speed = 18.6 m/s
Therefore,
\(2(- 4\ m/s^{2})s_{2} = (0\ m/s)^{2} - (18.6\ m/s)^{2}\\\\s_{2} = \frac{(18.6\ m/s)^{2})}{8\ m/s^{2}}\\\\s_{2} = 43.245\ m\)
So the total distance covered by the car before stopping is:
\(s = s_{1} + s_{2}\\s = 9.3\ m + 43.245\ m\\\)
s = 52.545 m