A race car starts from a rest to increases its speed to 23 m/s over a distance of 120 m. Calculate acceleration.

Answer:

= 201.53 meters

Explanation:

A car started from rest and accelerated at 9.54 m/s^2 for 6.5 seconds. How much distance was covered by the car?

Use the formula  d = \(\frac{at^{2} }{2} ,\)

where d is the distance, t is the time and "a" is the acceleration.
\(d=\frac{9*54*6*5^{2} }{2} = 201.53 m\)

The outside temperature is 24.9°C.

The outside temperature can be calculated using the given heat flow and the conductivity of ice.

To start, we can use the formula for heat flow:
heat flow = conductivity x area x (change in temperature/ thickness)

Plugging in the given values, we get:
299 = 2.40 x 1.00 x (outside temp - 0)/0.199

Simplifying, we get:
outside temp - 0 = 299 x 0.199/(2.40 x 1.00)
outside temp = 24.9°C

Therefore,  This means that if the temperature outside drops below this value, the ice on the lake will start to freeze even more, while if it rises above this value, the ice will start to melt. It is important to consider the temperature outside when determining the safety of walking or skating on a frozen lake, as well as for understanding the process of ice formation and melting.

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Answer:

C. Do not write anything next to it.

Explanation:

If an equation is already balanced there is no need to provide information of that.

The force responsible for the acceleration of the crate is the frictional force between the crate and the bed of the truck.

When the truck accelerates, the crate tends to remain at rest due to inertia. However, the frictional force between the crate and the bed of the truck acts in the forward direction, allowing the crate to accelerate along with the truck.

This frictional force is a result of the interaction between the surfaces of the crate and the truck bed. Without this frictional force, the crate would slide or move independently from the truck's acceleration.

The frictional force arises due to the microscopically rough surfaces of the crate and the truck bed. As the two surfaces are pressed against each other, intermolecular forces come into play, resulting in the generation of the frictional force

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Answer:

80%

Explanation:

The force reduces if the distance is doubled since force and distance are inversely proportional to each other.

Greater gravitational forces will be used to attract heavier things since the gravitational force is directly proportional to the mass of both interacting objects. Therefore, the gravitational attraction between two objects grows as their respective masses do as well. The force of gravity between two objects is equal to their respective masses multiplied by two. If one of the items triples in mass, the gravitational pull between them will also triple.

F= k m₁m₂ / d²

Gravitational Force = (Gravitational Constant × Mass of first object × Mass of the second object) / (Distance between the centre of two bodies)2.

if distance is doubled then force reduces, because distance is inversely proportional to the force.

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The refractive index, n of glass is 1.53.

The critical angle of a refracting medium such as glass is the angle at  no refracted ray is obtained for light passing through the medium between the boundary or interface of the medium and a less dense medium, rather an emergent ray which is per perpendicular to the normal is obtained.

Beyond the critical angle, total internal reflection occurs.

The refractive index of a medium is the ration of the velocity of light in the less dense medium to that in a denser medium.

Given that the critical angle of a medium is C;

Refractive index, n of the medium = 1/ sin C

The critical angle from glass to air is 40.5°

The refractive index of glass = 1/sin 40.5°

Refractive index, n of glass = 1.53

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By using the torque, the shear stress is 2.36 lb/ft².

We need to know about torque to solve this problem. Torque is the rotational equivalent of linear force. It can be determined as

τ = F x r

where τ is torque, F is perpendicular force and r is radius.

Shear stress can be calculated by torque

P = F / A

P = τ / (π.r³)

where P is shear stress, r is the radius.

From the question above, the parameter given are

τ = 200 ft.lb

d = 6 ft

Find the radius

r = 1/2 . d

r = 3 ft

Find the shear stress

P = τ / (π.r³)

P = 200 / (π.3³)

P = 2.36 lb/ft²

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Answer:

The momentum of the soccer ball will be twice that of the baseball.

Explanation:

If an object of mass \(m\) travels with a velocity of \(v\), the momentum \(p\) of that object will be \(p = m\, v\). Thus, if velocity is fixed, momentum will be portional to the mass of the object.

The mass of the soccer ball is twice that of the baseball: \((300 / 150) = 2\). Thus, when moving at the same velocity, momentum of the soccer ball will be twice that of the baseball.

The amount of heat that is gained by water is equal to the amount of heat loss by the ice. Therefore, we have the following relationship:

Where "Qw" is the heat of water and "Qi" is the heat of ice. The heat of water is given by:

The amount of heat of ice must be calculated for the two states, solid and liquid. For the solid-state the temperature will be from -30 degrees to 0 degrees, therefore, we have:

Where Ci is the specific heat of ice in solid-state and is equal to:

Replacing the values:

Solving the operations we get:

Now we need to determine the amount of heat that needs the ice to convert into liquid. This is given by:

Lf is the latent heat of ice and is equal to:

Replacing the values we get:

Solving the operations:

Now we need the amount of heat of liquid ice to its final temperature, this is given by:

Applying the relationship:

Cw is the specific heat of water and is equal to:

And the specific heat of ice is:

Replacing the values. The first two terms on the right side we already calculated and the final temperature is the same for both:

Solving operations:

Now we solve for the final temperature:

Subtracting 19835 to both sideS:

Now we add 1673Tf to both sides:

Now we divide both sides by 1882.2

Therefore, the final temperature is 20.57 °C. This value can be converted into Kelvin using the following relationship:

Replacing the temperature:

Therefore, the final temperature is 293.72 K.

Answer:

From Dr. Stephen Warren, University of Washington (8/22/2007): The world record for low temperature was set at Vostok Station, Antarctica, on 21 July 1983. Cerveny et al. (2007) give this temperature as -89.4°C in their Table 2, quoting Krause and Flood (1997), who gave the same value.

(Hope this answered your question!)

Answer:

heat and power

Explanation:

is the simultaneous production of electricity and heat both of which are used

Gravitational force between two masses m, and m, is represented as F = Gm₂ m₂ / r^2 where r = xi+yj + zkG, m, m₂ are nonzero constants and let's assume that I = 0

a) Calculation:For F = Gm₂ m₂ / r^2.

Using r = xi+yj + zk and let r^2 = x^2 + y^2 + z^2∴ F = Gm₂ m₂ / (x^2 + y^2 + z^2), Where G, m, m₂ are nonzero constants. Divergence of F = ∇ · F= 1/r^2(d/dx(r^2Fx) + d/dy(r^2Fy) + d/dz(r^2Fz))= 1/r^2(d/dx(r^2Gm₂ m₂ x/(x^2+y^2+z^2)^(3/2)) + d/dy(r^2Gm₂ m₂ y/(x^2+y^2+z^2)^(3/2)) + d/dz(r^2Gm₂ m₂ z/(x^2+y^2+z^2)^(3/2)))= 1/r^2(d/dx(r^2Gm₂ m₂ x/(x^2+y^2+z^2)) * (x^2+y^2+z^2)^(3/2) + d/dy(r^2Gm₂ m₂ y/(x^2+y^2+z^2)) * (x^2+y^2+z^2)^(3/2) + d/dz(r^2Gm₂ m₂ z/(x^2+y^2+z^2)) * (x^2+y^2+z^2)^(3/2))= 1/r^2(Gm₂ m₂ [2x(x^2+y^2+z^2)-3x^2]/(x^2+y^2+z^2)^(5/2) + Gm₂ m₂ [2y(x^2+y^2+z^2)-3y^2]/(x^2+y^2+z^2)^(5/2) + Gm₂ m₂ [2z(x^2+y^2+z^2)-3z^2]/(x^2+y^2+z^2)^(5/2))= 1/r^2(Gm₂ m₂ [(2x^2+2y^2+2z^2-3x^2)/(x^2+y^2+z^2)^(3/2)] + [2x^2+2y^2+2z^2-3y^2]/(x^2+y^2+z^2)^(3/2)] + [2x^2+2y^2+2z^2-3z^2]/(x^2+y^2+z^2)^(3/2)])= 1/r^2(Gm₂ m₂ [x^2+y^2+z^2]/(x^2+y^2+z^2)^(3/2))= 0.

Curl of F = ∇ × F= i(d/dy(Fz) - d/dz(Fy)) - j(d/dx(Fz) - d/dz(Fx)) + k(d/dx(Fy) - d/dy(Fx))= i(d/dy(Gm₂ m₂ z/(x^2+y^2+z^2)) - d/dz(Gm₂ m₂ y/(x^2+y^2+z^2))) - j(d/dx(Gm₂ m₂ z/(x^2+y^2+z^2)) - d/dz(Gm₂ m₂ x/(x^2+y^2+z^2))) + k(d/dx(Gm₂ m₂ y/(x^2+y^2+z^2)) - d/dy(Gm₂ m₂ x/(x^2+y^2+z^2)))= i(Gm₂ m₂ [-2xz]/(x^2+y^2+z^2)^(5/2)) - j(Gm₂ m₂ [-2yz]/(x^2+y^2+z^2)^(5/2)) + k(Gm₂ m₂ [(x^2+y^2-2z^2)]/(x^2+y^2+z^2)^(5/2))

b) Calculation:The line integral of F along a curve C can be evaluated by the following formula∫C F.dr = ∫∫ ( ∇ x F) ds, Where r is the position vector of the curve, s is the scalar parameter representing the curve, and the integral is evaluated from the initial point to the final point.

Using the curl of F obtained in part a) and for the surface with ∂S as C∫C F.dr = ∫∫ ( ∇ x F) ds= ∫∫ curl(F) ds= ∫∫ (-2xz i -2yz j + (x^2+y^2-2z^2)k) ds...[1]

Let's consider the surface S as a plane perpendicular to the z-axis of the form ax+by+c=0 and the curve C as the intersection of the plane and the cylinder x^2 + y^2 = a^2.

Let's choose the unit normal to the surface S as k (along the z-axis).

The curl of F is a vector field perpendicular to the plane and along the direction of k.

Thus the integral can be written as∫C F.dr = ∫∫ ( ∇ x F) . k ds= ∫∫ (x^2+y^2-2z^2) ds...[2]

Now let's evaluate the integral over the given plane ax+by+c=0. We can write x = t, y = (c-at)/b and z = 0, where t is the scalar parameter along the line of intersection of the plane and the cylinder (x^2 + y^2 = a^2).

Since the curve C is on the cylinder of radius a, we have x^2+y^2 = a^2 ⇒ t^2+(c-at)^2/b^2 = a^2On solving for t, we have t = (bc±ab √(a^2-b^2-c^2))/[a^2+b^2].

Substituting t in x and y, we get the curve C in the x-y plane as a function of the scalar parameter s asx = (bc±ab √(a^2-b^2-c^2))/[a^2+b^2]y = (c-at)/b= (c-(bc±ab √(a^2-b^2-c^2))/[a^2+b^2])/b.

Now we can evaluate the integral over the curve C, which is along the intersection of the plane and the cylinder.

Integral over C (x^2+y^2-2z^2) ds= ∫t₁^t₂ [(t^2 + [(c-at)^2]/b^2 - 2(0)^2)^(1/2)] dt= ∫t₁^t₂ [(a^2-b^2-c^2)t^2+2bc(c-at)+b^2c^2-a^2b^2]^(1/2) dt.

Now we can choose the value of t₁ and t₂ such that the square root in the integrand is minimized (so that the integral is path-independent).

This can be done by choosing the value of t that gives the minimum value of (a^2-b^2-c^2)t^2+2bc(c-at)+b^2c^2-a^2b^2 over the range of t from t₁ to t₂.

On differentiation with respect to t and equating to 0, we get the value of t = bc/(a^2+b^2).

Substituting this value of t in the integrand, we get the minimum value of the square root in the integrand to be |c| √(a^2+b^2)/|b|.

Thus the integral over C is given by∫C F.dr = ∫∫ (-2xz i -2yz j + (x^2+y^2-2z^2)k) ds= ∫∫ (x^2+y^2-2z^2) ds= ∫t₁^t₂ |c| √(a^2+b^2)/|b| dt= |c| √(a^2+b^2)/|b| (t₂-t₁).

Now we can see that the integral is path-independent as it depends only on the end points t₁ and t₂ and not on the path taken to reach them.

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Answer:

below

Explanation:

According to Newtons Second Law of Motion, also known as the Law of Force and Acceleration, a force upon an object causes it to accelerate according to the formula net force = mass x acceleration. So the acceleration of the object is directly proportional to the force and inversely proportional to the mass.

To measure motor units in the electromyography (EMG) simulator, the most appropriate method would be measuring the distance between two consecutive peaks of the same type in the green plot. So, option B is correct.

Electromyography is a technique used to evaluate and record the electrical activity produced by skeletal muscles. Motor units consist of a motor neuron and the muscle fibers it innervates. The EMG simulator generates signals that mimic the electrical activity of motor units.

By measuring the distance between two consecutive peaks of the same type in the green plot, we can obtain valuable information about the firing pattern and recruitment of motor units. The peaks represent the action potentials generated by individual motor units.

The distance between peaks can indicate the firing rate or the time interval between successive action potentials.

Counting the number of unique peaks in either the green or blue plot (options A and D) may not provide a comprehensive measure of motor units. It might only give an estimation of the number of active motor units, but it doesn't provide information about their firing patterns or recruitment.

Measuring the largest peak-to-peak value (option C) may not be as informative either because the size of the action potentials can vary depending on factors such as the proximity of the electrode to the motor unit or the intensity of the simulated muscle contraction.

Therefore, measuring the distance between two consecutive peaks of the same type in the green plot is a more reliable method to assess motor units in an EMG simulator, as it provides insights into their firing patterns and recruitment dynamics.

So, option B is correct.

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The correct choice is the third option.

This comes from the fact that the packing material cushions the impacts of the content in case of a fall.

Answer:

In what way is iron unique among the elements?

It has the lowest mass per nuclear particle.

Match words at the left to the correct blanks in the sentences on the right. Not all words will be used.

-The energy that drives the expansion of a star into a subgiant or red giant comes from HYDROGEN SHELL FUSION

-Stars with mass greater than about 8 solar masses are considered HIGH-MASS STARS

-The final stage of core fusion in a low-mass star is HELIUM FUSION

-Stars that are fusing hydrogen in their cores are MAIN-SEQUENCE STARS

-When it dies, a high-mass star explodes as a SUPERNOVA

-A star that is expanding (into a subgiant and then a giant) has a(n) INERT HELIUM CORE

-When it dies, a low-mass star expels a PLANETARY NEBULA

-Stars with masses less than about two solar masses are considered LOW-MASS STARS

Answer:

D

Explanation:

D) The velocity was forty meters in 10 seconds, or 4 meters per second.

The kinetic hypothesis of matter, which holds that all subatomic particles are constantly in motion, is supported by the observation of light specks moving around randomly in the box.

In this instance, the gas particles in the box are randomly colliding and moving, which is what is causing the smoke particles that were blown into the box to move. The movement of the gas particles in the box can be explained by the fact that the light specks, which are probably reflecting off the smoke particles, are also observed to be moving erratically and randomly.

This finding is consistent with the theory that matter is composed of minute, moving particles that collide and interact with one another in a chaotic, random manner. As the energy in the system drives the motion of the particles, it also emphasizes the significance of energy in this process.

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Answer: we divide the vector by its magnitude.

Explanation:

Answer:

2. Oxygenin blood: Iron is an essential element for blood production. About 70 percent of your body's iron is found in the red blood cells of your blood called hemoglobin and in muscle cells called myoglobin. Hemoglobin is essential for transferring oxygen in your blood from the lungs to the tissues.

4.Nitrogen: Nitrogen is in the air that we breathe into our lungs but only the oxygen in the air is transferred from the lungs to the bloodstream and nitrogen is breathed out as a waste product. ... So our red blood cells are adapted to carry Oxygen, whereas Nitrogen dissolves in tiny amounts.

Answer:

x=36.5 m

Explanation:

Rectangular Components of a Vector

A vector can be expressed as an ordered pair (x,y) where x is the x-coordinate, and y is the y-coordinate of a rectangular system.

It can also be given as a magnitude-angle pair (r,θ) where θ is measured from the positive x-axis. It's also known as polar coordinates.

The conversion from polar to rectangular coordinates is:

\(x=r\cos \theta\)

\(y=r\sin\theta\)

We are given the vector as a magnitude r=47.3 m and at an angle θ=39.4°. The x-component of the vector is:

\(x=47.3\cos (39.4^\circ)\)

Using a scientific calculator to find the trigonometric function:

\(x=47.3\cdot 0.7716\)

x=36.5 m

Answer:

280 W

Explanation:

ΔPE = change in potential energy (J)

m = mass (kg) = 25

g = gravity (m/s²) = 9.81

Δh = change in height (m) = 4

t = time taken (s) = 3.5

Relevant formulae:

\(ΔPE = mg(Δh) \\P= \frac{ΔPE}{t} \)

ΔPE = 25(9.81)(4)

ΔPE = 981

P = 981/(3.5)

P = 280.285...

Answer:the 90% is spent performing other functions

Explanation:

the distance, in inches, from the wall to the edge of the door is 8.2 inches.

We must utilise the reference angle that makes a right triangle with the wall and the edge of the door in order to determine the distance between them. The reference angle is 90° - (140°/2) = 20° since the door swings open by 140°.

To get the distance from the wall to the edge of the door, let's utilise trigonometry. Let x represent the distance from the door's edge to the wall. Next, we have:

sin(20°) = x/24

When we multiply both sides by 24, we obtain:

x = 24*sin(20°)

Calculating the answer, we discover:

x ≈ 8.2

Therefore, 8.2 inches or so separate the wall from the door's edge. The distance, rounded to the nearest tenth of an inch, is 8.2 inches.

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ANSWER

EXPLANATION

Parameters given:

Initial velocity, v0 = 78.4

Angle of projectile, θ = 52 degrees

(a) To find the flight time of the tennis ball, apply the formula:

where g = acceleration due to gravity

Hence, the total flight time of the tennis ball is:

(b) To find the maximum altitude of the ball during its flight, apply the formula:

Therefore, the maximum height attained by the tennis ball is:

(c) To find the horizontal distance the tennis ball travels, apply the formula:

Hence, the horizontal distance traveled by the tennis ball is:

(d) To find the final velocity of the tennis ball, apply the formula:

where h = initial height = 0 m

Hence, the final velocity of the tennis ball just before impact is:

a) Calculation of temperature at the fat-inner fur boundaryThe rate of heat flow is given by:

\(q =\frac{kA\Delta T}{d}\)

where, k = thermal conductivity; A = surface area; ΔT = temperature difference and d = thicknessSince the rate of heat flow is given to be 51.4 W, we can obtain the temperature difference from the given data.

\(ΔT = \frac{30.9 - 2.8}{\ln \frac{3.9}{1.6/2}} ≈ 3.6°C\)

Now, substituting the given values of A, d and k, we get

\(51.4 = \frac{0.200 \pi (1.6)^{2} \times 3.6}{0.039} × (T1 - 30.9)\)

where T1 is the required temperature at the fat-inner fur boundarySimplifying, we getT1 ≈ -9.7°Cb) Calculation of thickness of air layerAssuming the layer of air to be stationary and isothermal, the rate of heat flow can be calculated using the following equation:q = hAΔTwhere, h = heat transfer coefficientThe heat transfer coefficient, h can be calculated using the relation:

\(q = [\frac{kA\Delta T}{d} = hAΔT ⇒ h =\frac{k}{d}\\\)

Using this, we can obtain the heat transfer coefficient, which is approximately 0.7 W/(m².K)Using the relation above, we can write:

\(51.4 = 0.7 × (4π(1.6/2)²) × ΔT × d\)

where ΔT is the temperature difference and d is the thickness of the air layerSolving for d, we getd ≈ 1.2 cmTherefore, the thickness of the air layer should be around 1.2 cm so that the bear loses heat at a rate of 51.4 W.

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Answer: 8.10m/s

Explanation:

using second eq of motion s=ut+1/2at

2

as u=0, a=

t

2

2s

​

=

5.21

2

2∗110

​

=8.10m/s

2