The correct answer is - a. was a sign of danger.
Once the people saw that the ocean waters are receding and were living vast space without water behind them, they knew that something big and very dangerous will happen. And in fact it did. The water that was sucked in in the place were there was a crack on the ocean floor, got shot back under big pressure and it had very big speed, as well as having waves that were destroying anything on their way.
Answer:
Option (A)
Explanation:
Tsunamis are the series of large waves that are generated in the large water bodies such as seas and oceans, due to an earthquake, underwater explosion or landslide. These waves can rise up to a height of about hundreds of meters.
A receding ocean is a sign of danger that signifies that a tsunami is approaching. During this time the water level drops down unusually along the coastline. It is a kind of warning that is given to the people living in the coastal areas to evacuate it as soon as possible in order to save their lives.
Thus, the correct answer is option (A).
In one scene in the movie The Godfather II, a solid gold phone is passed around a large table for everyone to see. Suppose the volume of gold in the phone were equal to the volume of a 10-centimeter cube of gold. The density of gold is 19,300 kg/m3.
Could such a phone be casually passed around a table from hand to hand? What is the weight of the phone? 1 kg of mass is about 2.2 lb.
1. Yes; it weighs about 9 lbs.
2. No; it weighs about 90 lbs.
3. No; it weighs about 45 lbs.
4. Yes; it weighs about 4.5 lbs. ...?
Final answer:
Given the density of gold and the dimensions of a 10-centimeter cube, a solid gold phone would weigh about 45 lbs, making it too heavy to casually pass around a table. Therefore, the correct answer is 3.
Explanation:
The question asks if a solid gold phone, with a volume equal to a 10-centimeter cube of gold, could be casually passed around a table from hand to hand. Given the density of gold is 19,300 kg/m³, we first calculate the volume of the cube in cubic meters (m³) by converting its dimensions from centimeters to meters (0.1 m x 0.1 m x 0.1 m = 0.001 m³). Multiplying this volume by the density of gold gives us the mass of the gold phone (0.001 m³ x 19,300 kg/m³ = 19.3 kg). Converting this mass into pounds (1 kg ≈ 2.2 lbs), the weight of the phone is approximately 42.46 lbs.
Therefore, the correct answer is 3: No; it weighs about 45 lbs. Such a phone would be quite heavy and not easily passed around from hand to hand.
Which of the following is not an example of kinetic energy?
mechanical energy
nuclear energy
electrical energy
thermal energy
Final answer:
Nuclear energy is not an example of kinetic energy; it is a form of potential energy stored within the nucleus of atoms. Kinetic energy is associated with the motion of objects, while nuclear energy involves the potential stored and released during nuclear reactions.
Explanation:
Kinetic energy is the energy that an object possesses due to its motion. It can be expressed mathematically as KE = ½mv², where 'm' is the object's mass and 'v' is its velocity. Examples of kinetic energy include a moving vehicle, a spinning turbine, and the thermal energy of atoms and molecules moving within a substance. However, not all forms of energy listed are examples of kinetic energy.
Nuclear energy is different from kinetic energy. It is a form of potential energy that is stored within the nucleus of atoms and is released during nuclear reactions such as fission or fusion. Therefore, nuclear energy is the correct answer to the question, as it is not a form of kinetic energy.
Other forms of energy such as electrical energy and chemical energy can involve kinetic energy when charges travel through a conductor or when molecular bonds are broken and rearranged, respectively. However, at a fundamental level, these forms also incorporate potential energy components.
"A copper wire loop is constructed so that its radius, r, can change. It is held near a solenoid that has a constant current through it.
a. Suppose that the radius of the loop were increasing. Use Lenz' law to explain why there would be an induced current through the wire. Indicate the direction of that current.
b. Check your answer regarding the direction of the induced current by considering the magnetic force that is exerted on the charge in the wire of the loop. "
"A copper wire loop is constructed so that its radius, r, can change. It is held near a solenoid that has a constant current through it.
a. Suppose that the radius of the loop were increasing. Use Lenz' law to explain why there would be an induced current through the wire. Indicate the direction of that current.
b. Check your answer regarding the direction of the induced current by considering the magnetic force that is exerted on the charge in the wire of the loop. "
According to Lenz's law, an induced current is generated in a copper wire loop when its radius near a solenoid increases. The direction of this induced current opposes the increasing radius of the loop. This direction can also be determined by considering the magnetic force on the charges in the wire loop.
Explanation:a. According to Lenz's law, when the radius of the copper wire loop near the solenoid increases, an induced current is generated in the loop. This induced current flows in a direction that creates a magnetic field opposing the change in magnetic flux through the loop. Therefore, the direction of the induced current would be such that it opposes the increasing radius of the loop.
b. To check the direction of the induced current, we can consider the magnetic force on the charges in the wire loop. As the radius of the loop increases, the magnetic field due to the solenoid through the loop also increases. By applying the right-hand rule for the direction of the magnetic force on a moving charge, we find that the induced current in the loop would flow in a direction opposite to the increasing radius, in order to resist the change in magnetic field.
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In which phase transition do molecules directly move from state to state involving a vibration of particles in a fixed position to a state involving random movement of high speed particles
Evaporation
Sublimation
Freezing
Depostion
sublimation is the correct answer
A steam catapult launches a jet aircraft (from rest) from the aircraft carrier John C. Stennis, giving it a speed of 200 mi/h in 3.00 s.
(a) Find the average acceleration of the plane.
...?
What environmental factors affect kinetic energy and diffusion?
Dispersion is the separation of white light into separate colors by
A. differences in wavelength
B. differences in wave amplitude
C. the blocking of light
D. constructive interference
Dispersion is the separation of white light into separate colors based on differences in wavelength.
Explanation:Dispersion is the separation of white light into separate colors based on differences in wavelength. When light passes through a medium, such as a prism or a droplet of water, it is bent or refracted. However, different colors of light have different wavelengths, which causes them to refract at different angles. This results in the dispersion of white light into its constituent colors.
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Inside a NASA test vehicle, a 3.50kg ball is pulled along by a horizontal ideal spring fixed to a friction-free table. The force constant of the spring is 229 N/m. The vehicle has a steady acceleration of 5.00m/s^2, and the ball is not oscillating. Suddenly, when the vehicle's speed has reached 45.0m/s, its engines turn off, thus eliminating its acceleration but not its velocity. What is the frequency? ...?
Final answer:
The frequency of the spring in the NASA test vehicle is approximately 2.28 Hz.
Explanation:
To determine the frequency of the spring in the NASA test vehicle, we need to use the equation for the frequency of a mass-spring system:
f = 1 / (2π) * sqrt(k / m)
Where f is the frequency, k is the force constant of the spring, and m is the mass of the ball.
Plugging in the given values, we get:
f = 1 / (2π) * sqrt(229 N/m / 3.50 kg)
Calculating this, we find that the frequency is approximately 2.28 Hz.
What are 3 examples of elastic collisions?
Elastic collisions, where kinetic energy and momentum are conserved, can be demonstrated through the collision of glass marbles, steel blocks on ice, and carts with spring bumpers on an air track. These examples showcase momentum transfer and energy conservation in a nearly perfect manner, providing insight into the principles of physics.
Explanation:Examples of Elastic CollisionsElastic collisions are fascinating phenomena where total kinetic energy and momentum are conserved. Here are three examples:
Glass Marbles Collision: Two glass marbles suspended from the ceiling and colliding with each other nearly perfectly conserve kinetic energy and momentum. This setup provides a clear demonstration of how momentum is transferred from one object to another in an elastic collision.Steel Blocks on Ice: Two steel blocks sliding and colliding on ice represent another nearly perfect example of an elastic collision. Thanks to the reduced friction on icy surfaces, the blocks come very close to conserving kinetic energy fully.Carts with Spring Bumpers on an Air Track: This example involves two carts equipped with spring bumpers colliding on an air track. The air track’s nearly frictionless surface allows for a close approximation of an elastic collision, where kinetic energy is largely conserved.Although truly elastic collisions are rare in everyday experiences and more common in the microscopic realm of subatomic particles, these examples provide a good understanding of the concept within observable scenarios.
What is the function of the commutator in a DC motor?
Answer:
c for plato users
Explanation:
The answer is c, to change alternating current into direct current.
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When the switch is closed, what happens to the current in the circuit? (The intrinsic resistance of the inductor is zero.)
a.The current instantaneously becomes 2 .
b.The current instantaneously becomes 1 .
c.The current gradually increases from zero to 2 and then remains constant.
d.The current gradually increases from zero to 1 and then remains constant.
When a switch is closed in a circuit with an inductor, the current gradually increases from zero to a constant value. This is due to the property of inductors to initially oppose changes in current.
Explanation:The question asks about the behavior of current in a circuit when a switch is closed, specifically in relation to an inductor with zero intrinsic resistance. The correct answer is d. The current gradually increases from zero to 1 and then remains constant. When the switch is closed, establishing an electrical connection, the current does not become instantaneously high. Rather, it gradually increases. This is because the inductor initially opposes the change in current. As current continues to flow, this opposition decreases and the current increases, eventually reaching a constant value.
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Which statement about dwarf planets is true?
a. pluto was the first dwarf planet to be discovered.
b. all dwarf planets likely contain a mixture of rock and ice.
c. dwarf planets lie beyond the outer planets
Answer:
All dwarf planets likely contain a mixture of rock and ice
Explanation:
The true statement about dwarf planets is that Pluto was the first to be discovered. Dwarf planets share common features like orbiting the sun and having a near-spherical shape but have not cleared their orbits of other objects.
The true statement about dwarf planets is that Pluto was the first dwarf planet to be discovered. Dwarf planets are celestial bodies that meet two of the three criteria set by the International Astronomical Union (IAU) for being a planet: they orbit the sun and have sufficient mass for a nearly spherical shape, but they have not cleared their orbits of other objects. While not all dwarf planets are beyond the outer planets (Ceres, for example, is located in the asteroid belt between Mars and Jupiter), all discovered dwarf planets have a mixture of rock and ice, and with the exception of Ceres, they are found beyond Neptune. Pluto, which was initially classified as one of the major planets, became known as a dwarf planet due to the redefinition of what constitutes a planet in 2006.
ingrid kicks a football with an initial velocity at 12 m/s at an angle of 45 relative to the ground
The question involves analyzing the motion of a football being kicked with given initial velocity and angle in Physics.
Physics: The question involves analyzing the motion of a football being kicked with given initial velocity and angle.
Example: Ingrid kicks a football with an initial velocity of 12 m/s at an angle of 45 degrees relative to the ground.
Concepts: Projectile motion, velocity, angle, and distance traveled are essential in solving such problems in physics.
The law of conservation of mass states that _______________________________.
The law of conservation of mass states that mass is neither created nor destroyed in chemical reactions, remaining constant.
The law of conservation of mass states that:
1. Mass cannot be created or destroyed in a chemical reaction or a physical change.
2. The total mass of substances before a reaction must equal the total mass of the substances after the reaction.
3. At the atomic level, this law implies that the number and types of atoms present in the reactants must equal the number and types of atoms in the products.
4. This principle holds true for closed systems where no mass is exchanged with the surroundings, although in nuclear reactions, mass can be converted into energy according to Einstein's famous equation E=mc²..
5. The conservation of mass is a fundamental principle in chemistry and underpins our understanding of chemical reactions and the behavior of matter in various processes.
A cream tangerine is thrown directly upward past three evenly spaced windows of equal heights. Rank the windows according to (a) the average speed of the cream tangerine while passing them, (b) the time the cream tangerine takes to pass them, (c) the magnitude of the acceleration of the cream tangerine while passing them, and (d) the change in velocity in the speed of the cream tangerine during the passage, greatest first. I just need help with C.
The magnitude of the acceleration of the cream tangerine as it passes by each window is constant at approximately 9.8 m/s² due to Earth's gravity.
Explanation:You asked about the magnitude of the acceleration of a cream tangerine as it passes by three evenly spaced windows. When any object is thrown upward or downward close to the Earth's surface, it is accelerated by gravity. This acceleration is constant and has a magnitude of approximately 9.8 m/s² downward. This means that no matter which window the cream tangerine is passing, the magnitude of its acceleration will be the same because gravity is a constant force close to the surface of the Earth. Therefore, when ranking the windows according to the magnitude of acceleration of the cream tangerine while passing them, they will all be the same and thus tied for first place.
pls.. help me with this i really need it.. pls. A gas in a cylinder expands from a volume of 0.110 m3 to 0.320 m3. Heat flows into the gas just rapidly enough to keep the pressure constant at 1.65 x 105 Pa during the expansion. The total heat added is 1.15 x 105 J. (a) Find the work done by the gas. (b) Find the change in internal energy of the gas. (c) Does it matter whether the gas is ideal? Why or why not?
a)
At constant pressure, the work done for gas to expand is given by:
W = PΔV
⇒W = 1.65 × 10⁵Pa × (0.320 - 0.110)m³= 3.46 × 10⁴J
b)
The total heat (Q) added to the system is used in work done and the remaining energy goes into internal energy.
ΔU = ΔQ-ΔW
⇒ΔU = 1.15 ×10⁵J - 3.46 × 10⁴J = 0.8 × 10⁵ J
c)
It does not matter that the gas is ideal or real because the work done would remain same. It would vary for real gases only at very high pressure.
(a). The work done by the gas is [tex]\boxed{3.47 \times {{10}^4}\,{\text{J}}}[/tex].
(b). The change in the internal energy of the gas is [tex]\boxed{8.03 \times {{10}^4}\,{\text{J}}}[/tex].
(c). There is no effect of the gas being ideal gas or real gas on the work done by the gas.
Further Explanation:
Given:
The initial volume of the gas is [tex]0.110\,{{\text{m}}^{\text{3}}}[/tex] .
The final volume of the gas is [tex]0.320\,{{\text{m}}^{\text{3}}}[/tex] .
The constant pressure at which the expansion of the gas takes place is [tex]1.65 \times {10^5}\,{\text{Pa}}[/tex] .
The amount of heat added to the gas is [tex]1.15 \times {10^5}\,{\text{J}}[/tex].
Concept:
Part (a):
The expansion of the gas is taking place at constant pressure. Therefore, the work done by the gas is:
[tex]W = P\left( {{V_f} - {V_i}}\right)[/tex]
Here, [tex]P[/tex] is the pressure and [tex]{V_f}[/tex] is the final volume and [tex]{V_i}[/tex] is the initial volume of the gas.
Substitute the values of [tex]P[/tex] , [tex]{V_i}[/tex] and [tex]{V_f}[/tex] in above expression .
[tex]\begin{aligned}W&= \left( {1.65 \times {{10}^5}} \right) \times \left( {0.320 - 0.110} \right)\\&= 3.465 \times {10^4}\,{\text{J}}\\&\approx 3.{\text{47}} \times {\text{1}}{{\text{0}}^4}\,{\text{J}}\\\end{aligned}[/tex]
Therefore, the work done by the gas is [tex]\boxed{3.47 \times {{10}^4}\,{\text{J}}}[/tex]
Part (b):
The change in internal energy of the gas is given by the first law of thermodynamics:
[tex]\begin{aligned}\Delta Q = \Delta U + W \hfill\\\Delta U = \Delta Q - W \hfill\\\end{aligned}[/tex]
Here, [tex]\Delta Q[/tex] is the heat added, [tex]\Delta U[/tex] is the change in internal energy of system and [tex]W[/tex] is the work done by the gas.
Substitute the values of [tex]\Delta Q[/tex] and [tex]W[/tex] in above equation.
Part (c):
The ideal gas or the real gas does not affect the process of the expansion of gas because the change in energy of the gas is given by the First law of thermodynamics. The first law of thermodynamics is based on the conservation of energy.
The energy of a system will always remain conserved whether it has the real gas or the ideal gas.
Thus, there is no effect of the gas being ideal gas or real gas on the work done by the gas.
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Answer Details:
Grade: High School
Subject: Physics
Chapter: Law of Thermodynamics
Keywords: Ideal gas, cylinder, first law of thermodynamics, pressure constant, 0.110m^3 to 0.320 m^3, expansion, change in internal energy, work done by gas.
If a galaxy is located 200 million light years from Earth, what can you conclude about the light from that galaxy?
A. The light will take 200 million years to reach Earth.
B.The light will travel 200 million kilometers per second to reach Earth.
C.The light will travel a total of 300,000 kilometers to reach Earth.
D.The light will travel a total of 200 million kilometers to reach Earth.
The answer is not D. Just got it incorrect on my quiz.
Answer:
A. The light will take 200 million years to reach Earth.
Explanation:
a 1250 kg car accelerates from rest to 6.13m/s over a distance of 8.58m calculate the average force of traction
Final answer:
To find the average force of traction for the car, you can use the work-energy principle to determine the work done, which equals the change in kinetic energy. The work done is equal to the force multiplied by the distance, and from this, the average force can be calculated. The average force of traction in this case is 2723.17 N.
Explanation:
To calculate the average force of traction for a 1250 kg car that accelerates from rest to 6.13 m/s over a distance of 8.58 m, we can use the work-energy principle. This principle states that the work done by a force on an object is equal to the change in kinetic energy of the object.
First, let's find the final kinetic energy (KE) of the car:
KE = 0.5 * m * v^2
KE = 0.5 * 1250 kg * (6.13 m/s)^2
KE = 23369.8125 J (joules)
The work done (W) by the traction force is also the change in kinetic energy, so W = KE = 23369.8125 J. Since work is defined as the force multiplied by the distance (W = F * d), we can rearrange the formula to solve for the average force (F):
F = W / d
F = 23369.8125 J / 8.58 m
F = 2723.17 N (newtons)
Therefore, the average force of traction that the car experienced was 2723.17 N.
what is the best definition of the term due process of law?
Due process of law is a legal concept that mandates the fair and equal application of the law, ensuring that no individual is deprived of life, liberty, or property without proper legal procedures and protections, as stated in the Fifth and Fourteenth Amendments of the U.S. Constitution.
The best definition of the term due process of law is a legal principle that ensures the government respects all legal rights owed to a person. According to the Fifth and Fourteenth Amendments of the U.S. Constitution, no one shall be "deprived of life, liberty, or property without due process of law." This includes two aspects: procedural due process, which pertains to the methods and processes the government must follow, and substantive due process, which relates to the government's obligations to treat individuals fairly and not to violate certain fundamental rights.
two trains start from towns 240 mi apart and travel towards each other on parallel tracks. they pass each other 1.6 hr later. If one train travels 10 mph faster than the other, find the speed of each train ...?
Which vector best represents the force that could act concurrently with force A to produce force B
2 or second vector best represents the force that could act concurrently with force A to produce force B.
What is force?A force is an effect that can alter an object's motion according to physics. An object with mass can change its velocity, or accelerate, as a result of a force. An obvious way to describe force is as a push or a pull. A force is a vector quantity since it has both magnitude and direction.
A resultant force vector is described as a single vector that has the same consequence as several other vectors taken together.To create the resulting force vector, two vectors facing the opposite direction are subtracted from one another. Here, the vector B is pointing in the opposite direction of the vector A, and the resulting force vector is called R.
2 or second vector best represents the force that could act concurrently with force A to produce force B.
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What particles are added together to get the atomic mass?
The range of all electromagnetic radiation is known as the
HR diagram
Electromagnetic spectrum
sources of light chart
radio wave graph
A Styrofoam slab has thickness h and density ρs. When a swimmer of mass m is resting on it, the slab floats in fresh water with its top at the same level as the water surface. Find the area of the slab. (Use any variable or symbol stated above along with the following as necessary: ρw for the density of water.)
This question involves the concepts of the bouyant force, weight, and volume.
The area of the slab is "[tex]\frac{m}{h(\rho_w-\rho_s)}[/tex]".
In order for the styrofoam slab to float on the water, the buoyant force acting on it must be equal to its weight:
[tex]Weight = Buoyant\ Force\\(m+M)g=\rho_w Vg\\m+M=\rho_w V[/tex]
where,
m = mass of swimmer
A = area of styrofoam slab = ?
h = thickness of strrofoam slab
[tex]\rho_s[/tex] = density of styrofoam slab
[tex]\rho_w[/tex] = density of water
M = mass of styrofoam slab = [tex]Ah\rho_s[/tex]
V = volume of styrofoam slab = Ah
Therefore,
[tex]m+(Ah\rho_s) = Ah\rho_w\\m= Ah(\rho_w-\rho_s)\\\\A=\frac{m}{h(\rho_w-\rho_s)}[/tex]
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When a person jumps from tree to ground, what happens to the momentum of the person upon striking the ground? ...?
Upon striking the ground, the person's momentum goes to zero as they stop, with the momentum transferred to the Earth. Bending the knees upon landing extends the stopping distance, reducing the force experienced.
Explanation:When a person jumps from a tree to the ground, the momentum of the person upon striking the ground changes drastically. Momentum is a product of the mass of an object and its velocity. In this case, the person carries momentum as they fall, due to their velocity and mass. Upon impact with the ground, this momentum is quickly reduced to zero because the person comes to a stop. According to the law of conservation of momentum, the momentum lost by the person is transferred to the Earth.
However, because the Earth's mass is so immense compared to that of the person, the change in the Earth's velocity is negligible and unobservable. If the person lands with stiff knees, a large force is experienced over a shorter stopping distance, while bending the knees extends the stopping distance, resulting in a smaller force felt by the person.
A hot air balloon is traveling vertically upward at a constant speed of 2.8 m/s. When
it is 29 m above the ground, a package is
released from the balloon.
After it is released, for how long is the
package in the air? The acceleration of gravity
is 9.8 m/s^2.
Answer in units of s
What is its speed just before impact with the
ground?
Answer in units of m/s
A gas is at 5 Kelvin and 1 m3. The temperature is raised to 10 Kelvin. What is the new volume?
2 m3
2 m
5 m
Answer:
The new volume of the gas is 2 m³
Explanation:
It is given that,
Initial temperature, [tex]T_1=5\ K[/tex]
Initial volume, [tex]V_1=1\ m^3[/tex]
Final temperature, [tex]T_2=10\ K[/tex]
We need to find the new volume. The Charles law gives the relation between the temperature and the volume of the gas.
i.e
[tex]V\propto T[/tex]
[tex]\dfrac{V_1}{T_1}=\dfrac{V_2}{T_2}[/tex]
[tex]V_2=\dfrac{V_1}{T_1}\times T_2[/tex]
[tex]V_2=\dfrac{1}{5}\times 10[/tex]
[tex]V_2=2\ m^3[/tex]
So, the new volume of the gas is 2 m³. Hence, this is the required solution.
The force of attraction between two objects, which is related to the object's mass is the definition of
Answer:
Explanation:
The gravitation force of attraction between the two bodies is directly proportional tp the product of masses of two bodies and inversely proportional to the square of distance between them.
When compared to others, how is a greater velocity represented on a motion map?
with shorter vectors
with longer vectors
with larger dots
with smaller dots
Answer:
with longer vectors
Explanation:
In any motion map of vectors we know that length of vectors is used to represent the magnitude
while the direction of the vector is represented by the angle made by the vector.
So here we have to represent the larger or greater velocity
This represents the magnitude of the vector to be more
so the correct answer would be
"with Longer vectors" we can show or represent velocity vector of greater velocity.
The position of a particle moving along the x axis varies in time according to the expression x = 4t 2, where x is in meters and t is in seconds. Evaluate its position at the following times.
(a)t=2.10s
______m
(b)t=2.10s +Δt
xf=________m
(c)Evaluate the limit of Δx/Δt as Δt approaches zero to find the velocity at t = 2.10 s.
_______m/s ...?
a) The particle's position at t = 2.10 s is 17.64 meters, and the velocity at this time is 16.8 m/s.
b) The position at a later time t = 2.10 s + Δt can be found by squaring the entire term (t + Δt) and multiplying by 4.
c) The limit of Δx/Δt as Δt approaches zero to find the velocity at t = 2.10 s. is 16.8 m/s.
The equation of motion for the particle as it moves along the x-axis is x = 4t² where x is in meters and t is in seconds.
(a) To find the position at t = 2.10 s, we simply plug the value of t into the equation: x = 4(2.10)² = 4(4.41) = 17.64 meters.
(b) The position xf at time t = 2.10 s + Δt is given by x_f = 4(t + Δt)².
(c) To find the velocity at t = 2.10 s, we take the limit of Δx / Δt as Δt approaches zero.
This is equivalent to the derivative of x with respect to t, which gives us the velocity: v = dx/dt = d/dt(4t²) = 8t. Substituting t = 2.10 s gives us v = 8(2.10) = 16.8 m/s.
(a) At t = 2.10 s, the position of the particle is 35.28 m. (b) At t = 2.10 s + [tex]\(\Delta t\)[/tex], the final position [tex](\(x_f\)) is \(4t^2 + 8.4t\Delta t + 4(\Delta t)^2\)[/tex] m. (c) The limit of [tex]\(\frac{\Delta x}{\Delta t}\) as \(\Delta t\)[/tex]approaches zero at t = 2.10 s is 16.8 m/s.
Explanation:(a) Substitute t = 2.10 s into the given expression [tex]\(x = 4t^2\)[/tex] to find [tex]\(x = 4(2.10)^2 = 35.28\)[/tex] m.
(b) For [tex]\(x_f\)[/tex], we use the expression [tex]\(x_f = 4t^2 + 8.4t\Delta t + 4(\Delta t)^2\)[/tex] to account for the change in time [tex](\(\Delta t\)).[/tex]
(c) To find the velocity at t = 2.10 s, evaluate the limit of [tex]\(\frac{\Delta x}{\Delta t}\)[/tex] as [tex]\(\Delta t\)[/tex]approaches zero. Taking the derivative of [tex]\(x = 4t^2\)[/tex] with respect to t gives the instantaneous velocity, which is 16.8 m/s.
Understanding how to evaluate position at specific times and finding instantaneous velocity provides insights into the kinematics of particle motion.