Adhere to the images given:

Angular velocity (in rev/s) after a 15.0 kg child gets onto it by grabbing its outer edge is 1.575 rad/s.

The angular velocity of the merry-go-round after a child gets on it is equal to the angular velocity of the child plus the angular velocity of the merry-go-round.

The angular velocity of a rotating object can be calculated using a formula:

ω = ω + (m/r)

where ω is the original angular velocity, m is the mass of an object that's been added to it, r is its radius, and (m/r) is the change in mass divided by its radius. When we plug in our values for this problem, we get:

ω = 0.350 rad/s + ((15 kg)/(1.8 m)) rad/s

= 0.350 rad/s + 1.25 rad/s

= 1.575 rad/s

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Considering a quadratic equation to model the height of the car, we have that:

Considering an acceleration = gravity of -9.8m/s², the equation for the height is given as follows:

h(t) = -4.9t² + v(0)t + h(0).

In which:

Considering the values of these parameters for this problem, of v(0) = 20, h(0) = 115, the equation is:

h(t) = -4.9t² + 20t + 115.

At the maximum height point, we have that:

The velocity function is:

v(t) = v(0) - gt

v(t) = 20 - 9.8t.

Which is the linear function graphed at the end of the answer.

The cat hits the ground at t > 0 for which h(t) = 0, hence:

-4.9t² + 20t + 115 = 0.

Which is a quadratic equation with coefficients given by:

a = -4.9, b = 20, c = 115.

Using a calculator, the positive solution for this equation is:

t = 7.30s.

At this instant, the velocity is:

v(t) = 20 - 9.8(7.3) = -51.54 m/s.

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12.5kg is the mass that would result in critical damping.

The ability of a damper to resist motion is shown by its damping coefficient, which measures the effectiveness of the damper. where c is the damping coefficient and is expressed in newton seconds per meter.

The damping coefficient is a term that has the formula where is a constant. This damping is equivalent to the kind of motion resistance and energy loss experienced when a piston with perforations is moved through a cylinder filled with a viscous fluid, like oil.

Force F = Kx

K = F/x

K = 3/1.5

K = 2N/m.

c² - 4mk = 0

m = c²/4k

m = 10²/4×2

m = 100/8

m = 12.5kg.

12.5kg is the mass that would result in critical damping.
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Uniform line movement

Data:

V = 80km/h

T = 15m = 0.25 h

d = ?

We perform a conversion from minutes to hours.

           15 m * 1 h/60 m = 0.25 h

The formula for uniform motion is:

                      V = d/t

We clear for distance:

                  d = v * t

                  d = 80 km/h * 0.25 h

                  d = 20 km

The distance traveled in that time is 20 km.

Work done on sphere is 10500 J.

Kinetic energy = 1/2 [tex]iw^{2}[/tex] + 1/2 [tex]m v^{2}[/tex]

I = 2/5 [tex]m R^{2}[/tex]

w = [tex]\frac{v}{r}[/tex]

Now, put these values in formula KE = 1/2 [tex]iw^{2}[/tex] + 1/2 [tex]m v^{2}[/tex]

KE = 10500 J

Now, by work energy theorem

Work done = 10500 - 0 = 10500 J

Hence, Work done on sphere is 10500 J.

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The inverse square relation implies that  force resulting from gravity between two masses will decrease as the square of the distance between the two masses increases.

The force of gravity between any two objects is given by,

F = GM₁M₂/R²

Where,

M₁ and M₂ are the masses of the bodies.

R is the distance between them.

We know, if the masses are constant. then the force of gravity will be inversely proportional to the square of the distance between them.

This is what inverse square relation means here.

As the force of gravity and the square of the distance are inversely proportional to each other,

So, when the square of the distance between the masses increases, the force of gravity between the decreases.

Hence of all the options provided, b is the correc0,t which says, the force will decrease on increasing the inverse square of the distance.

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Answer:

Explanation:

Given:

V₀ = 2 m/s

V = 20 m/s

Δt = 12 s

__________

a - ?

The acceleration of the van:

a = ΔV / Δt = (V - V₀) / Δt

a = (20 - 2) / 12 = 18 / 12 ≈ 1.5 m/s²

R0 is the original resistance. Thus, R = 9(6.0Ω) = 54 Ω.

Electric current flowing through and potential difference across an electrical component can be used to determine its resistance.

Ohm's Law, which depicts the connection between potential difference, current, and resistance:

V = I R, where V is the potential difference (in volts), V I is the current (in amps), A R is the resistance (in ohms), and

The following equation can be changed to determine the resistance:

R = V ÷ I

According to Ohm's equation, I = V/R, the behaviour of the material may be predicted if the resistance remains constant over a significant range of voltage. The definition above applies to both AC and DC applications of resistors, despite the fact that it deals with DC current and voltage.

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The ratio of I sub A to I sub B is 4.

How can you calculate the ratio of A to B?

A/B would be your formula if you were comparing one data point (A) to another data point (B). This indicates that you are multiplying information A by information B. For instance, your ratio will be 5/10 if A is 5 and B is 10. How do we determine each wheel's moments of inertia (around the axis of symmetry) I is equal to 1 over 2 times m times R squared is used to compute the moments of inertia for both masses and radii. We simply use a common factor to cancel. So 4:2=2:1 . The simplest representation of the ratio 4 to 2 is the ratio 2 to 1. Additionally, since each pair of numbers has the same relationship, the ratios are equivalent.

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The velocity of an object is the ratio of distance to the time. The graph shows, an increase in distance with the increase in time. This linearity make the velocity constant. Hence, the option D is correct.

Velocity of a substance is the measure of distance travelled per unit time. Thus it is the ratio of distance to time.In physics, velocity is the rate of speed.

Velocity = distance/time.

Hence, as the time taken for the travel increases velocity will decreases. In the given graph at each point distance shows linear relation with the time and it obtains a straight line.

Therefore, the distance is increasing with increase in time means the velocity is not changing and it remains constant. Hence, option D is correct.

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The coefficient of the kinetic friction between the box and the floor is μk 0.21.

Friction is the force resisting the relative motion of strong surfaces, fluid layers, and fabric elements sliding against every different. There are several sorts of friction: Dry friction is a pressure that opposes the relative lateral movement of two solid surfaces in touch.

Calculation:-

Given,

mass = 40 Kg

Applied force F = 85 N

initial velocity u = 0 (rest)

distance moved = 1.4 meter

Final velocity = 1 m/s

coefficient of kinetic friction =?

Normal force = N = mg = 400 N

v² = u² +2as

a = v²/2s

  = 1/2×1.4

 = 0.36 m/s²

F = μkN

μk = F/N

     = 85/400

     0.21

Friction is a shape of touch pressure. It exists between the surfaces which are in touch. The frictional force relies upon on the person of the surface in contact. The rougher the floor, the greater the friction is involved. The frictional force is proportional to the urgent pressure, this is the weight of the body. it's far impartial of the place of the touch.

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The car speeds remains constant.

Using the following equation for momentum:

Pi=Pf

(c=car and r=rock)
              McVc + MrVr = McV'c + MrV'r

Initially
                         Vc=Vr=Vi
and since rocks are being dropped directly downward, final momentum of the rocks (being dropped one at a time) should be zero because their falling down, out of the railroad car.
So:
Vi( Mc+Mr) = McV'c V'c = [Vi(Mr+Mc)] / Mc

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The speed of the lorry 4 seconds later, given it was moving with uniform acceleration of 1.5 m/s² is 12 m/s

We'll begin by listing out the various parameters obtained from the question. This is shown below:

The final speed of the lorry can be obtained as follow:

a = (v - u) / t

1.5 = (v - 6) / 4

Cross multiply

v - 6 = 1.5 × 4

v - 6 = 6

Collect like terms

v = 6 + 6

v = 12 m/s

Thus, from the calculation made above, the final speed of the lorry is 12 m/s

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Gravity's role in the tectonic plate motion can be described on the basis of ridge push and slab pull of tectonic plates.

Ridge push refers to gravitational sliding. It is a driving force for plate motion in plate tectonics, occurring at mid-ocean ridges as the result of the rigid lithosphere sliding down the hot and raised asthenosphere below mid-ocean ridges.

Slab pull is a pulling force that is exerted by a cold and dense oceanic plate plunging into the mantle. The term for the process of a tectonic plate descending into the mantle is subduction. Subduction may emerge due to gravity.

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We must understand both inertia and gravity to find a solution.

What is inertia?

The matter has an attribute called inertia that makes it resist changes in velocity (speed and direction). Newton's first law of motion states that an object moving at a certain speed will stay there unless an outside force acts upon it.

What is gravity?

A planet or other body's gravitational field pulls objects toward its center. The force of gravity is what keeps every planet in its orbit around the sun.

A vertical circle spun while holding a bucket full of water prevents the water from spilling out due to inertia.

Keep the bucket in place as the water tries to fly off.

Therefore we can conclude that it is false.

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The movement of the beam of light is an illustration of distance and rates

The beam of light along the shoreline is moving at 261.5 km per minute when it is 1 km from P

The ratio of the distance traveled to the time required is used to compute average speed, which is the rate at which distance changes in relation to time.

[tex]\frac{d\theta}{dt}[/tex] = 8 rev min⁻¹ = 16 [tex]\pi[/tex] rad min⁻¹

tan [tex]\theta[/tex] = [tex]\frac{x}{5}[/tex]

Differentiate both sides with respect to t

[tex]sec^2 (\theta) \frac{d\theta}{dt} = \frac{1}{5} \frac{dx}{dt}[/tex]

[tex]\frac{d\theta}{dt}[/tex] = 16 [tex]\pi[/tex]

Then,

[tex]\frac{dx}{dt}[/tex] =  [tex]sec^2 (\theta) X 80\pi[/tex]

From the question, x = 1. calculate the hypotenuse (h) side of the triangle, using the following Pythagoras theorem.

[tex]h^2 = 1+ 5^2\\[/tex]

h =[tex]\sqrt{26}[/tex]

sec ([tex]\theta[/tex]) = [tex]\frac{\sqrt{26} }{5}[/tex]

Substitute sec ([tex]\theta[/tex]) = [tex]\frac{\sqrt{26} }{5}[/tex] in [tex]\frac{dx}{dt}[/tex] =  [tex]sec^2 (\theta) X 80\pi[/tex].

[tex]\frac{dx}{dt} = (\frac{\sqrt{26} }{5} )^2 . 80\pi[/tex]

= 83.2 [tex]\pi[/tex] = 261.48

Hence, the beam of light along the shoreline is moving at 261.5 km per minute when it is 1 km from P.

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Answer:Blood type AB Rh+

Explanation:

solid particles vibrate and slip past each other when they become liquid.

The spring compresses if it is an elevator accelerating upwards at 3g is Option A. a)16x

Acceleration is the rate of change of the velocity of an item with appreciation to time. Accelerations are vector portions. The orientation of an item's acceleration is given by the orientation of the net pressure appearing on that object.

Calculation:-

Gravitational acceleration = g

Spring constant of the spring = k

Mass of the first block = m1

Compression of the spring due to the first block = X1

m1g = kX1

Mass of the second block = 4m1

Upward acceleration of the elevator = 3g

The force from the spring on the second block = F

Compression of the spring due to the second block in the elevator = X2

From the free-body diagram of the 4m1 block,

(4m1)(3g) = F - 4m1g

F = 16m1g

kX2 = 16m1g

kX2 = 16(kX1)

X2 = 16X1

Compression of the spring due to a 4m1 block placed on it in an elevator accelerating upwards at 3g = 16X1.

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The amount of constant acceleration needed to accomplish this is:

6 m/s2.

Given;

The car will drive a distance of d = 1.2 km

To convert 1.2 km to m

1.2 x 1000

= 1200 m.

beginning speed of the car, where u = 0.

Travel time, t = 20 s

To get the constant acceleration, use the following kinematic equation;

d = ut + ¹/₂at²

1200 = 0 + ¹/₂(20)²a

1200 = 400 /2

1200 = 200a

a = 1200 / 200

a = 6 m/s²

Therefore, 6 m/s² of constant acceleration is needed to accomplish this.

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The amount of constant acceleration needed to accomplish this is 6 m/s2.

A velocity change that does not alter over time is referred to as a constant acceleration. A car's average acceleration remains steady at 20 mph per minute even if it increases its speed by 20 mph in one minute and another 20 mph the next.

Given;

The car will drive a distance of d = 1.2 km

To convert 1.2 km to m

1.2 x 1000

= 1200 m.

beginning speed of the car, where u = 0.

Travel time, t = 20 s

To get the constant acceleration, use the following kinematic equation;

d = ut + ¹/₂at²

1200 = 0 + ¹/₂(20)²a

1200 = 400 /2

1200 = 200a

a = 1200 / 200

a = 6 m/s²

Therefore, 6 m/s² of constant acceleration is needed to accomplish this.

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Displacement from the center line for minimum intensity is 1.35 mm , width of the slit  is 0.75 so  Wavelength of the light  is 506.25.

When a wave is bent by an obstruction whose dimensions are similar to the wavelength, diffraction is observed. We can disregard the effects of extremes because the Fraunhofer diffraction is the most straightforward scenario and the obstacle is a long, narrow slit.

This is a straightforward situation in which we can apply the

Fraunhofer single slit diffraction equation:

y = mλD/a

Where:

y = Displacement from the center line for minimum intensity =  1.35 mm

λ =  wavelength of the light.

D = distance

a = width of the slit = 0.75

m = order number = 1

Solving for λ

λ = y + a/ mD

Changing the information that the issue has provided:

λ = 1.35 * 10^-3 + 0.75 * 10^-3 / 1*2  

=5.0625 *10^-7 = 506.25

so

Wavelength of the light 506.25.

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Substances in a mixture keep their separate properties, but in a compound the parts are bonded and do not keep their separate properties.

Mixtures contains elements and compounds without any fixed ratio and not by any means of chemical bonds. The elements and compounds are physically mixed and so they will be visibly distinct.

Compounds contains elements in a fixed ratio and is connected by chemical bonds. They only contain one type of molecule. Since they are chemically combined the particles appear as one and is not visibly distinct.

Therefore, substances in a mixture keep their separate properties, but in a compound the parts are bonded and do not keep their separate properties.

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The answers include the following:

This is referred to as a group of stars that form a perceived pattern or outline and are usually given names and an example is hydra.

The Zenith as the name implies is known as the overhead point in the sky which is usually hardly seen while the constellation which is closest to this point tonight is Polaris due to the position thereby making it the most appropriate choice.

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The semi-infinite body shall be considered as a system that is bounded by one surface and that extends to infinity in other directions.

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One plate of the capacitor holds a positive charge Q and the other plate holds a negative charge -Q.

When charging a capacitor, a single electron is first added to one side of the capacitor and then the charge moves so that the electron has an electric field that repels the other electrons.

This electric field penetrates space and pushes electrons into the other plate, giving that plate an induced positive charge. This will give you the same amount of charge on both plates.

So one plate of the capacitor holds a positive charge Q and the other plate holds a negative charge -Q.

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The equal and opposite force for the force of the elevator floor pushing up on the person as described by Newton's third law is the weight and the reaction force from its effect.

This is referred to as a device which is used in the vertical transportation of goods and people among the floors in a buildings.

When an individual steps into the elevator, the weight acts on it and it is known as a downward force while the reaction acts upward in an opposite reaction as described by Newton's third law in this scenario.

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An obstruction is just ahead on the shoulder. Your front wheel leaves the roadway at a high speed. You countersteer when the front tire touches the roadway.

Countersteer is usually done by the cyclists and motorcyclists to turn at higher speeds. It is advisable to be done only on the race tracks. This is because the two wheels do not follow the same path during turning and it may affect other vehicles on normal roads. The rider must be leaned in the direction of turn in order to complete the turn. As the front wheel leaves at a higher speed, countersteering is done when the front wheel touches the ground.

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dT = -T^4/(2mD^2)dP

P = W/T = FD/T = (m a)D/T

dP = -maD/T^2 dT

dT = -T^2/(maD)dP

V = aT

D = 1/2 a T^2

a = 2D/T^2

dT = -T^4/(2mD^2)dP

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The Cosmic Microwave Background radiation, or CMB for squat, is a faint glow of light that fills the universe, falling on Earth from each direction with nearly uniform intensity.

The CMB represents the heat leftover from the Big Bang. You can't see the CMB with your bare eye, but it is everywhere in the universe. It is unseen to humans because it is so cold, just 2.725 degrees above total zero. Planck mapped out the warp in the CMB due to gravitational lensing caused by dark matter's existence. The CMB materialized as an electromagnetic fog on optical telescopes and as a static hum on radio telescopes. The CMB will certainly emerge slightly different from any distant galaxy,

So we can conclude that The Cosmic Microwave Background (CMB) is the cooled remains of the first light that could ever travel freely throughout the Universe.

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If the moon orbits the Earth at a distance of 3.84 x 10⁸ on a path that takes 27.3 days to complete, its centripetal acceleration will be 2.7x 10⁻³ m/s².

A body moving in a circular path at a high rate of speed is said to be experiencing centripetal acceleration. We can calculate the moon's centripetal acceleration using the centripetal acceleration formula.

We are informed that the moon is approximately 3.84 x 10⁸ miles away from Earth and that a full rotation of the moon takes 27.3 days.

The distance traveled by the moon in 27.3 days is its velocity.

v = x/t

v = 2 πr/t

v = 2.41x10⁹/2.35x10⁶

v = 1025.5

The radius is 3.84 x 108 m and the velocity is 1,025.5 m/s. Here, we will determine the centripetal acceleration of the moon.

[tex]a_{c}[/tex] = v²/r

[tex]a_{c}[/tex] = (1025.5)²/3.84 x 10⁸

[tex]a_{c}[/tex] = 2.7 x 10⁻³

We now know the centripetal acceleration of the moon to be 2.7 103 m/s².

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