(a) The magnitude of A is 14 and magnitude of B is 14.2.
(b) The magnitude of A - B is 19.95.
(c) The sum of A and B is 7i + 18j + 5k
(d) The magnitude of A + B is 19.95.
What is the magnitude of A and B?The magnitude of A and B is calculated as follows;
| A | = √ ( 4² + 6² + 12² )
| A | = 14
| B | = √ ( 3² + 12² + 7² )
| B | = 14.2
The magnitude of A - B is calculated as follows;
A - B = ( 4i + 6j + 12k ) - (3i + 12j - 7k)
A - B = ( i - 6j + 19 k )
|A-B| = √ (1² + 6² + 19²) = 19.95
The sum of A and B is calculated as follows;
A + B = ( 4i + 6j + 12k ) + (3i + 12j - 7k)
A + B = ( 7i 18j + 5k )
The magnitude of A + B is calculated as follows;
|A+B| = √ (7² + 18² + 5²) = 19.95
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b. A bird in air looks a fish vertically below it inside the water from a distance 5m from surface of water and fish lies at depth 4m from the surface of water. IF Mw= 4/3, what is the distance of fish as observed by bird?
Answer:
the distance of the fish (as seen by the bird) is greater than the actual distance.
Reason-
it is due to the apparent depth and differences between the refractive indices.
Have a nice day!
A small block sits at one end of a flat board that is 2.50 m long. The coefficients of friction between the block and the board are μs = 0.450 and μk = 0.400. The end of the board where the block sits is slowly raised until the angle the board makes with the horizontal is α0, and then the block starts to slide down the board.
Hi there!
In order for a block to begin sliding, the force due to STATIC friction must be overcome.
In this instance, the following forces are acting on the block ALONG the axis of the incline.
Force due to gravity (Fg)Force due to STATIC friction (Fs)Force due to gravity:
On an incline, the component of the force due to gravity contributing to the object's downward movement is equivalent to the horizontal (sine) component.
\(F_g = Mgsin\theta\)
Force due to static friction:
The force due to friction is equivalent to the normal force multiplied by the coefficient of friction.
The normal force is the cosine component (perpendicular to the incline), so:
\(N = Mgcos\theta\\\\F_s = \mu_sMgcos\theta\)
To find the minimum angle for the block to begin sliding, we can set the two forces equal to 0. They work in opposite directions (let down the incline be negative and up the incline be positive).
\(\Sigma F = F_s - F_g\\\\0 = F_s - F_g\\\\0 = \mu_sMgcos\theta - Mgsin\theta\\\\Mgsin\theta = \mu_sMgcos\theta\)
Cancel out 'Mg' and rearrange to solve for theta.
\(sin\theta = \mu_scos\theta\\\\tan\theta = \mu_s\\\\\theta = tan^{-1}(\mu_s) = tan^{-1}(.45) = \boxed{24.228^o}\)
The potential energy of a body of mass m is given by U(x) = -mgx + 1/2kx^2. The corresponding force is
Answer:
F = (mg - kx) i ^
Explanation:
Force and potential are related
F = - (\(\frac{dU}{dx}\) i ^ + \frac{dU}{dy} j ^ + \frac{dU}{dz} k ^)
in this exercise we are told that the potential is
U = - m g x + ½ kx²
let's make the drive
\frac{dU}{dx} = -mg + kx
\frac{dU}{dy}= 0
\frac{dU}{dz} = 0
we substitute
F = (mg - kx) i ^
What is the velocity of a car that travels from mile marker 32 on I-10 to mile marker 312 on I-10 in a time of 2 hours and 45 minutes? SYW!
Answer:
101.81818 MPH
Explanation:
d. The mass of the boy is the same in all places because mass does not depend
on gravity.
True or False
(Science)
Explanation:
Remember, even if you weigh less because of a change in gravity's force on your body, your body's mass is still the same. As your body grows, you will have more mass, which also means you will weigh more. That's because when you're on the earth, the amount of gravity that pulls on you stays the same.Thank you for marking me Brainlist ☺️Answer:
true . it depends tho weight depends on gravity .
Drag each label to the correct location on the chart.
Based on Newton's law of universal gravitation, complete the following table.
tum. All rights reserved.
distance increases
mass increases
Gravity Increases When:
distance decreases mass decreases
Reset
Gravity Decreases When:
Next
When mass grows and distance contracts, gravity increases. Additionally, as distance and mass decrease, gravity also reduces.
Which Newtonian principle is universal?Manning's universal law of gravity asserts that every atom in the cosmos pulls more or less every particle with a pressure along a connecting line, to put it in modern terms. The force is equal to the ratio of the wavelength between them and found to be proportional to the combination of their masses.
Is there a universal rule governing gravity?What exactly does the Law of Gravitation apply to According to Newton's theory of Universal Gravitation, every particle in the cosmos is drawn to every other particle with a force that is equal to the product of their masses and inversely to their distance from one another.
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When mass grows and distance contracts, gravity increases. Additionally, as distance and mass decrease, gravity also reduces.
Which Newtonian principle is universal?Manning's universal law of gravity asserts that every atom in the cosmos pulls more or less every particle with a pressure along a connecting line, to put it in modern terms. The force is equal to the ratio of the wavelength between them and found to be proportional to the combination of their masses.
Is there a universal rule governing gravity?What exactly does the Law of Gravitation apply to According to Newton's theory of Universal Gravitation, every particle in the cosmos is drawn to every other particle with a force that is equal to the product of their masses and inversely to their distance from one another.
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The net force experienced by an object is increased. What affect does this have on the acceleration of the object?
Answer:
The acceleration of an object depends directly upon the net force acting upon the object, and inversely upon the mass of the object. As the force acting upon an object is increased, the acceleration of the object is increased. As the mass of an object is increased, the acceleration of the object is decreased.
Explanation:
hope it helps pls give me brainless
A 500 kg car is moving at 30 m/s. The driver sees a barrier ahead. If the car takes 100 m to come to rest, what is the magnitude of the force necessary to stop the car?
How do you solve this question?
Answer:
F = 2250 [N]
Explanation:
In order to solve this problem, we must first use the following equation of kinematics.
\(v_{f}^{2} =v_{o}^{2}-2*a*x\)
where:
Vf = final velocity = 0 (come to rest)
Vo = initial velocity = 30 [m/s]
a = acceleration or desaceleration [m/s²]
x = distance = 100 [m]
\((0)=30^{2} -2*a*100\\900 = 200*a\\a = 4.5 [m/s^{2}]\)
Now we must use the following equation of kinetics, which is based on Newton's second law that explains that the sum of forces on a body is equal to the product of mass by acceleration.
∑F = m*a
where:
F = force [N]
m = mass = 500 [kg]
a = acceleration = 4.5 [m/s²]
\(F = 500*4.5\\F = 2250 [N]\)
The energy that a substance contains is
a. equilibrium
b. heat
c. thermal energy
d. entropy
The energy that a substance contains is known as heat. Thus, the correct option for this question is B.
What is Entropy?Entropy may be characterized as the measurement of the degree of randomness or in other words, it is the increase in the disorganization within a system. It is the measure of a system's thermal energy per unit temperature that is unavailable for doing useful work.
Equilibrium is a state of balance between opposing forces or actions that is either static or dynamic. It symbolizes the circumstance of being balanced in nature.
Thermal energy is a type of energy that is significantly contained within a system that is responsible for its temperature. Heat is the flow of thermal energy.
Therefore, the energy that a substance contains is known as heat. Thus, the correct option for this question is B.
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1
Find the x-component of this
vector:
Help Resources
0.250 m
18.4°
Skip
Remember, angles are measured from
the +X axis.
x-component (m)
Answer:
x-component = 0.237 [m]
Explanation:
In order to solve this problem in an easy way, we must first make a sketch of the vector and its respective angle with the X-axis, in the attached image we can see that sketch.
Since the X component of the vector is needed, this component can be found by means of the cosine of the angle and its hypotenuse.
x-component = 0.250*cos(18.4)
x-component = 0.237 [m]
Answer:
x = 0.237
y = -0.0789
Explanation:
A car is initially moving at 100 m/s and decides to gun it. They accelerate at a rate of 20 m/s/s for 10 seconds. How far did they travel during this time period?
Answer:
dx = 2000 [m]
Explanation:
To solve this problem we must use the following equation of kinematics.
\(dx =v_{o}*t +\frac{1}{2} *a*t^{2}\)
where:
dx = distance [m]
Vo = initial velocity = 100 [m/s]
a = acceleration = 20 [m/s²]
t = time = 10 [s]
dx = 100*10 + 0.5*20*10²
dx = 2000 [m]
Note: the positive sign in the above equation means that the car is increasing its velocity.
A quarterback throws a pass at an angle of 35° above the horizontal with an initial speed of 25 m/s. The ball is caught by the receiver 2.55 seconds later. Determine the distance the ball was thrown.
The distance the ball was thrown is 52.22m by A quarterback throws a pass at an angle of 35° above the horizontal with an initial speed of 25 m/s. The ball is caught by the receiver 2.55 seconds later.
How to calculate distance?Every motion under constant acceleration is projectile motion
Angle above horizontal Ф = 35°, initial speed v1 = 25m/s , time 2.55s
Substituting value in the below equation
x=x₁ + (v₁*cosθ)(t)+1/2 *a*t²
a= 0 as acceleration in horizontal direction is zero
x= 25*cos(35)*2.55
x=52.22 m
Projectile motion is a form of motion in which object influenced when it is launched into the gravitational force from the surface of Earth along a curved path.
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Which of the following organisms is not found in savannas?
a.
cheetah
b.
pangolin
c.
prairie chickens
d.
hyena
The answer is C- prairie chickens
prairie chickens organisms is not found in savannas. The correct option is c.
Savannas are typically characterized by the presence of tall grasses and a few scattered trees. The climate in this ecosystem is hot and dry, with a pronounced wet and dry season. Prairie chickens are not found in savannas.Here's why prairie chickens are not found in savannas:Savannas are typically found in tropical regions and are characterized by tall grasses and a few scattered trees. In contrast, prairies are found in temperate regions and are characterized by shorter grasses and a greater number of trees. Prairie chickens are a species of bird that are primarily found in prairie habitats. These birds are adapted to life on the open plains and feed on a variety of insects and seeds. While prairie chickens may share some similarities with the animals found in savannas, they are not typically found in this type of ecosystem.
option C is the correct answer.
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John is conducting an experiment that involves melting ice cubes. Which of the following is most important for John to collect reliable data?
A.The outcome needs to be controlled.
B.An unbiased observer must witness the experiment.
C.Technology needs to be used to determine the results.
D.Only one variable should be tested during the experiment.
Answer:
Hmmmm
Explanation:
Answer:
B
Explanation:
A roller coaster is at a peak of 20m and has a mass of 900kg. What is the potential energy of the roller coaster?
O 100000 J
10000 J
O 9.8 J
O 176400 J
The potential energy of the roller coaster is 176,400 J (joules).
The potential energy of an object is given by the formula PE = mgh, where PE is the potential energy, m is the mass of the object, g is the acceleration due to gravity, and h is the height or vertical position of the object.
In this case, the roller coaster is at a peak of 20m and has a mass of 900kg. The acceleration due to gravity, g, is approximately 9.8 \(m/s^2\).
Using the formula, we can calculate the potential energy:
PE = mgh
= (900 kg)(9.8 \(m/s^2\))(20 m)
= 176,400 J
Therefore, the potential energy of the roller coaster is 176,400 J (joules).
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You will need to know that Force (N) is equal to mass (kg) multiplied by acceleration (m/s2) for this problem. A fearless space explorer has discovered a new planet with a frictionless surface! He pushes a large crate with a mass of 220kg a distance of 5.3 km, as he does so, it accelerates at a rate of 2m/s2. How much work has our intrepid hero done?
The intrepid hero has done 2.332 x Joules of work in pushing the crate.
To ascertain the work done by the traveler, we first need to find the power he applied on the case. As per Newton's subsequent regulation, force is equivalent to mass times speed increase, so the power applied by the traveler on the container is:
Force = mass x speed increase = 220 kg x 2 = 440 N
Then, we really want to work out the distance the case was moved. The pilgrim pushed the box a distance of 5.3 km, or 5,300 m.
At long last, we can compute the work done by the pioneer utilizing the equation:
Work = force x distance = 440 N x 5,300 m = 2.332 x 10^6 Joules
Thusly, the valiant legend has done 2.332 x Joules of work in pushing the case.
The space pilgrim takes care of business on the case by applying a power that makes it speed up. The work done is equivalent to the power duplicated by the distance over which the power is applied. Involving the recipe for force, F=ma, and the given qualities for mass and speed increase, we can ascertain the power applied. Then, at that point, involving the recipe for work, W=Fd, and the given distance, we can ascertain the work done. The work done by the adventurer is 2.332 x J.
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What units must be used for mass in
the calculation of kinetic energy?
Answer:
The units of kinetic energy are mass times the square of speed, or kg⋅m2/s2 kg ⋅ m 2 /s 2. But the units of force are mass times acceleration, kg⋅m/s2 kg ⋅ m/s 2, so the units of kinetic energy are also the units of force times distance, which are the units of work
Explanation:
EDGE 2021
AV ASSIGNMENT what is the length of wire whose resistivity, 3x10^6 ohm with the r=0.2mm with a given Value of 15.5 ohm's Resistance.
basics of gravitation:
Planet a exerts a force on planet b. What can be said about the magnitude and direction of the gravitational force planet b exerts on planet a?
Answer:
Explanation:
According to Newton's Law of Gravitation, the gravitational force between two objects is always mutual, meaning that the force that one object exerts on the other is equal in magnitude but opposite in direction.
This means that if planet A exerts a gravitational force on planet B, then planet B will also exert a gravitational force on planet A. The magnitude of this force will be equal to the magnitude of the force that planet A exerts on planet B, but the direction will be opposite.
For example, if planet A exerts a gravitational force on planet B that is pulling planet B towards planet A, then planet B will also exert a gravitational force on planet A that is pulling planet A towards planet B. The magnitude of these two forces will be equal, but the directions will be opposite.
hat he sais
Answer:w
Explanation:
Your car’s wheels are 65.0 cm in diameter, and the wheels are spinning at an angular velocity of 136 rad/s. How fast is your car moving (assume no slippage)?
The car is moving with the linear velocity of 44.2 m/s.
We have the diameter of car wheels as 65 cm which are spinning at an angular velocity of 136 rad/s.
We have to determine how fast is the car moving or its linear velocity.
What is Angular Velocity ?Angular velocity is defined as the rate of change of angular position of a rotating body.
\(\omega = \frac{d\theta}{dt}\)
According to question, we have -
diameter of car wheels = 65 cm
Therefore, the radius will be = 32.5 cm
Angular velocity = 136 rad/s
We know that -
v = r\(\omega\)
v = 32.5 x 136
v = 4420 cm/s
v = 44.2 m/s
Hence, the car is moving with the linear velocity of 44.2 m/s.
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Mr. Bateman creates a standing wave in the front of the classroom with the spring. S nodes form. The distance from Mr. Bateman to the cabinet is 6m. If a student times the spring moving back and forth and gets 0.2s for one cycle of the spring, how fast are the
waves moving?
Answer:
The speed of a wave is equal to the wavelength divided by the period. The wavelength is the distance between two consecutive nodes, and the period is the time it takes for one complete cycle of the wave.
In this case, the wavelength is 6 m and the period is 0.2 s. Therefore, the speed of the wave is 30 m/s.
The answer is 30 m/s.
Explanation:
4. Calculate the total resistance of the circuit if R1=4 Ω, R2=30 Ω, R3=10Ω, R4=5Ω Determine the current strength if the circuit is connected to a voltage source with a voltage of 56 V
The total resistance of the circuit is 49 Ω. The current strength in the circuit, when connected to a voltage source of 56 V, is approximately 1.14 A.
To calculate the total resistance of the circuit, we need to determine the equivalent resistance of the resistors connected in a series.
Given:
R1 = 4 Ω
R2 = 30 Ω
R3 = 10 Ω
R4 = 5 Ω
Calculate the equivalent resistance (RT) of R1 and R2, as they are connected in series:
RT1-2 = R1 + R2
RT1-2 = 4 Ω + 30 Ω
RT1-2 = 34 Ω
Calculate the equivalent resistance (RTotal) of RT1-2 and R3, as they are connected in parallel:
1/RTotal = 1/RT1-2 + 1/R3
1/RTotal = 1/34 Ω + 1/10 Ω
1/RTotal = (10 + 34) / (34 * 10) Ω
1/RTotal = 44 / 340 Ω
1/RTotal ≈ 0.1294 Ω
RTotal ≈ 1 / 0.1294 Ω
RTotal ≈ 7.74 Ω
Calculate the equivalent resistance (RTotalCircuit) of RTotal and R4, as they are connected in series:
RTotalCircuit = RTotal + R4
RTotalCircuit = 7.74 Ω + 5 Ω
RTotalCircuit ≈ 12.74 Ω
Therefore, the total resistance of the circuit is approximately 12.74 Ω.
To determine the current strength (I) when connected to a voltage source of 56 V, we can use Ohm's Law:
I = V / RTotalCircuit
I = 56 V / 12.74 Ω
I ≈ 4.39 A
Therefore, the current strength in the circuit, when connected to a voltage source of 56 V, is approximately 4.39 A (or 1.14 A, considering significant figures).
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Students have 4 different pairs of sunglasses, each with lenses where the polarization filter is oriented in different directions (indicated by the direction of lines drawn on the lenses below). They are planning to ride rafts down a river on a sunny day where there is lots of glare on the water. Which pair would they want to wear to eliminate the glare from the sun
Answer:
the lens you must select has an angle of 143º measured with respect to the horizontal, this angle is 53º with respect to the vertical.
Explanation:
The glare is caused by the reflection of light in the water, the polarization of the reflected light is polarized in a direction parallel to the surface of the water, the polarization is total for the angles
n = tan \(\theta_{p}\)
\theta_{p} = tan⁻¹ n
the refractive index for seawater is 1.33
\theta_{p}= tan⁻¹ 1.33
\theta_{p} = 53º
for this angle the light is totally polarized, for the other angles the polarization is partial.
Based on this, the lenses must eliminate this polarization, so its polarization direction must have 90º with respect to this polarization,
\theta_{lens} = 53 +90
\theta_{lens}= 143º
Therefore, the lens you must select has an angle of 143º measured with respect to the horizontal, this angle is 53º with respect to the vertical.
A lens that could work is one that is polarized 45º with respect to the vertical.
The glass that is worn to eliminate glare must be able to remove glare away from the user.
What are sunglasses?The term sunglasses refers to the kind of glasses that are worn to prevent glare from the sun. This is because the glasses are made of polaroid materials that eliminate glare.
The question is incomplete as the sunglasses are not shown. However, the glass that is worn to eliminate glare must be able to remove glare away from the user.
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A sprinter with a mass of 70 kg accelerates at a rate of 5 m/s2. What force is the sprinter exerting?
Answer:
The force exerted by the sprinter can be calculated using Newton's second law of motion, which states that the force acting on an object is equal to its mass multiplied by its acceleration:
F = m * a
where:
F is the force
m is the mass of the object (70 kg)
a is the acceleration (5 m/s^2)
Plugging in the values, we get:
F = 70 kg * 5 m/s^2
F = 350 N
So, the sprinter is exerting a force of 350 N. This is the force that the sprinter's legs are applying to the ground, propelling them forward and producing the acceleration.
iron has more mass than gold. Does this mean that the density of iron is greater
Answer:
There masses are identical "I hope this helps"
A soccer ball accelerated at a rate of 500(m)/(s^(2)) when it was kicked by a player. The soccer ball had a mass of 0.5kg, and it reached a speed of 40(m)/(s). During this acceleration, what was the net force applied on the soccer ball to the nearest newton? [8.2E] Enter your answer in the space.
Net force applied on the soccer ball was approximately 250 N (newtons) when it was kicked by the player.
What is Newton's second law of motion?We use Newton's second law of motion, which states that net force (F_net) applied to an object is equal to the product of its mass (m) and acceleration (a):
F_net = m * a
In this case, mass of the soccer ball is given as 0.5 kg and the acceleration is 500 (m)/(s²), so:
F_net = 0.5 kg * 500 (m)/(s²) = 250 N
Therefore, net force applied on the soccer ball was approximately 250 N (newtons) when it was kicked by the player.
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PLEASE HELP ASAP! 100 PTS! 5 QUESTIONS - Pls Show Your Work!!!!
1. Two carts are pushed apart with a spring attached to one of the carts. The carts have masses of 1.2 kg and 2.5 kg. The 2.5 kg cart (Cart B) has a velocity of 1.5 m/s after they spring apart. Find the velocity of the 1.2 kg. cart.
2. An 6,000 kg train car moves at 20.0 m/s until it bumps into a stationary 6,000 kg car and latches onto it. What is the speed of the two cars linked together?
3. A single 1,000 kg train car moving at 5.0 m/s collides with the back of two 1,000 kg train cars linked together. It latches onto the car it strikes as the two parts of the coupled cars exert forces on each other. What is the speed of the cars immediately afterward?
4. A 15.0 kg cart and a 20 kg cart are locked together with a compressed spring between them. They are then released so that the spring pushes the two carts apart. The 20 kg cart is moving at 5.0 m/s afterward. How fast is the 15.0 kg cart moving?
5. A firecracker stuck into a 150 g apple explodes and sends five apple fragments in different directions. The vector sum of momenta 1, 2, 3, and 4 is found from a video of the event to have components px = 1.20 kg m/s, py = 0.80 kg m/s (with no other component). The mass of the fifth fragment is 0.050 kg. What is its velocity right after the explosion?
The total momentum, both before and after, is (2m)(v/2) = mv, which is equal to the total mass times the velocity of the centre of mass.
How do you find the momentum of two objects after a collision?The system's centre of mass was at v/2 before to the collision because one automobile was travelling at v and the other at zero before the collision. Because the total momentum is equal to the total mass times the velocity of the centre of mass, the total momentum before and after equals (2m)(v/2) = mv.
K.E1 = 1/2 m1u21 + 1/2 m2u22 is the kinetic energy of the masses prior to contact. The collision's kinetic energy, however, is given by K.E2 = 1/2 (m1 + m2) v2. However, in accordance with the rule of energy conservation: 1/2 m1u21 + 1/2 m2u22 = 1/2 (m1+ m2) v2 + Q.
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In a DC generator, the generated emf is directly proportional to the
In a DC generator, the generated electromotive force (emf) is directly proportional to the rotational speed of the generator's armature and the strength of the magnetic field within the generator.
This relationship is described by the equation for the generated emf in a DC generator:
Emf = Φ * N * A * Z / 60
Where:
Emf is the generated electromotive force (in volts),
Φ is the magnetic flux density (in Weber/meter^2\(meter^2\) or Tesla),
N is the number of turns in the armature winding,
A is the effective area of the armature coil (in square meters),
Z is the total number of armature conductors, and
60 is a constant representing the conversion from seconds to minutes.
From this equation, we can see that the generated emf is directly proportional to the magnetic flux density (Φ) and the product of the number of turns (N), effective area (A), and the total number of armature conductors (Z). This means that increasing any of these factors will result in a higher generated emf.
The magnetic flux density (Φ) can be increased by using stronger permanent magnets or increasing the strength of the field windings in the generator.
The number of turns (N) and the effective area (A) are design parameters and can be optimized for a specific generator. Increasing the number of turns or the effective area will result in a higher generated emf.
Similarly, the total number of armature conductors (Z) can be increased to enhance the generated emf.
By controlling and optimizing these factors, the generated emf in a DC generator can be increased, resulting in higher electrical output. However, it is important to note that there are practical limits to these factors based on the design and construction of the generator.
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If the distance travelled by a body in time t is given by x = at + bt^2, then what will be the acceleration of the body?
Answer:
Explanation:
the general form of the position equation with constant acceleration is
s = s₀ + v₀t + ½at²
where
s = position at time = t
s₀ = original position with respect to the selected origin
v₀ = velocity at t = 0
a = constant acceleration
comparing to the equation
x = + at + bt²
shows that
s₀ = 0
v₀ = a
½a = b
a = 2b
acceleration will be twice the b value
8. Which of these substances has the lowest density?a. Water vaporb. Boiling waterc. Room-temperature waterd. Ice
ANSWER:
a. Water vapor
STEP-BY-STEP EXPLANATION:
The density of water vapor is less than the density of a water liquid, in the case of ice, we can see how ice floats on liquid water, which indicates that it has a lower density.
The water obtains its highest density at 4°C, being equal to 1000 kg/m³, in that state it is still liquid water, at room temperature, it is a little lower but it is still a higher density than water vapor, boiling water and ice.
Water vapor would have a lower density than all of them since it is a gas, so the correct answer is a. Water vapor