A block of ice with mass 5.50 kg is initially at rest on a frictionless, horizontal surface. A worker then applies a horizontal force F⃗ to it. As a result, the block moves along the x-axis such that its position as a function of time is given by x(t)=αt2+βt3, where α = 0.210 m/s2 and β = 2.04×10−2 m/s3 .
A. Calculate the velocity of the object at time t = 4.50 s .
B. Calculate the magnitude of F⃗ at time t = 4.50 s .
Express your answer to three significant figures.
C. Calculate the work done by the force F⃗ during the first time interval of 4.50 s of the motion.
Express your answer to three significant figures.

Answer:

 I = 7.96 W / m²

Explanation:

The light bulb emits a power of P = 100W, this power is distributed over the surface of a sphere, thus the emission is in all directions.

Intensity is defined by power per unit area

            I = P / A

The area of ​​a sphere is

         A = 4π r²

we substitute

         I = P / (4π r²)

in this case it tells us that the distance is r = 1 m

let's calculate

        I = 100 / (4π 1²)

        I = 7.96 W / m²

Answer:

halve the slit separation

Explanation:

As we know that

In YDS experiment, the equation of fringe width is as follows

[tex]\beta = \frac{\lambda D}{d}[/tex]

where,

D denotes the separation in the middle of screen and slits

d denotes the distance in the middle of two slits

And to increase the Δx we have to decrease the d i.e, the distance between the two slits

Hence, the first option is correct

Explanation:

The separation between the interference fringes on the screen increases because the distance of the screen from the slit is increased. Therefore option (a) is  correct.

The separation between the interference fringes on the screen increases because  the distance of the screen from the slit is increased, which is contradictory. Therefore option (b) is incorrect.

The separation between the interference fringes on the screen increases because  the distance of the screen from the slit is increased, which is contradictory. Therefore option (c) is incorrect.

The separation between the interference fringes on the screen increases because  the distance of the screen from the slit is increased, which is contradictory. Therefore option (d) is incorrect.

The separation between the interference fringes on the screen increases because  the distance of the screen from the slit is increased, which is contradictory. Therefore option (e) is incorrect.

Answer:

It will be half that if the first wave

Explanation:

Because the wave speed remains the same, the result of doubling the frequency is that the wavelength is half as large as it

Answer:

λ_A = 700 nm ,   m_B = m_a 2

Explanation:

The expression that describes the diffraction phenomenon is

         a sin θ = m λ

where a is the width of the slit, lam the wavelength and m an integer that writes the order of diffraction

a) They tell us that now lal_ A m = 1

         a sin θ = λ_A

coincidentally_be m = 2

          a sin  θ = m λ_b

as the two match we can match

         λ _A = 2 λ _B

         λ_A = 2 350 nm

         λ_A = 700 nm

b)

For lam_B

       a sin  λ_A  = m_B  λ_B

For lam_A

        a sin θ_A = m_ λ_ A

to match they must have the same angle, so we can equal

           m_B  λ_B = m_A  λ_A

           m_B = m_A  λ_A / λ_B

           m_b = m_a 700/350

           m_B = m_a 2

Answer:

Everything in the Universe is made up of matter and energy. Matter is anything that has mass and occupies space. ... Energy is the ability to cause change or do work. Some forms of energy include light, heat, chemical, nuclear, electrical energy and mechanical energy.

Explanation:

Answer:

cognitive behavioral therapy

Explanation:

Answer:

Ultraviolet light from the sun.

Explanation:

This is an example of radiation.

Answer:

X-Ray

Explanation:

x-Ray is an example of radiation.

Answer:

cost_cost = $ 96

Explanation:

In this exercise we have units in the groin system and the SI system, to avoid problems let's reduce everything to the SI system

         performance = 21 miles / gallon (1,609 km / 1 mile) (1 gallon / 3,785 l)

         perfomance= 8,927 km / l

now let's use a direct rule of proportions (rule of three). If a liter travels 8,927 km, how many liters are needed to travel the 2015 km

          #_gasoline = 2015 km (1l / 8.927 km) = 225.72 liters

Now let's find the total cost of fuel. Ns indicates that $ 0.11 = 1 peso and the liter of fuel costs 5.8 pesos

            cost_litre = 5.8 peso ($ 0.11 / 1 peso) = $ 0.638

             cost_gasoline = #_gasoline   cost_litro

             cost_gasoline = 225.72   0.638

             cost_gasoline = $ 144

This cost is for the one way trip, the total round trip cost is

             cost_total = 2 cost_gasoline

             cost_total = $ 288

Now let's look for the cost in the vehicle, you and two people will go, for which a total of 3 people will go, so the cost per person is

                cost_person = total_cost / #_people

                cost_person = 288/3

                cost_cost = $ 96

Explanation:

Given that,

Separation between two long parallel conductors, r = 11 cm = 0.11 m

Current in first wire, [tex]I_1=3\ A[/tex]

Current in second wire, [tex]I_2=8\ A[/tex]

(a) The magnetic field created by I₁ at the location of I₂ is given by :

[tex]B_{12}=\dfrac{\mu_o I_1}{2\pi r}\\\\B_{12}=\dfrac{4\pi \times 10^{-7}\times 3I_1}{2\pi \times 0.11}\\\\B_{12}=5.45\times 10^{-6}\ T[/tex]

(b) Magnetic force per unit length exerted by [tex]I_1[/tex] on [tex]I_2[/tex] is given by :

[tex]\dfrac{F}{l}=\dfrac{\mu_o I_1I_2}{2\pi r}\\\\\dfrac{F}{l}=\dfrac{4\pi \times 10^{-7}\times 3\times 8}{2\pi \times 0.11}\\\\\dfrac{F}{l}=4.36\times 10^{-5}\ N/m[/tex]

(c) The magnetic field created by I₂ at the location of I₁ is given by :

[tex]B_{21}=\dfrac{\mu_o I_2} {2\pi r}\\\\B_{12}=\dfrac{4\pi \times 10^{-7}\times 8}{2\pi \times 0.11}\\\\B_{12}=1.45\times 10^{-5}\ T[/tex]

Hence, this is the required solution.

Answer:

factor that bug maximum KE change is 0.52284

Explanation:

given data

vertical distance = 6.5 cm

ripples decrease to =  4.7 cm

solution

We apply here formula for the KE of particle that executes the simple harmonic motion that is express as

KE = (0.5) × m × A² × ω²     .................1

and kinetic energy is  directly proportional to square of the amplitude.

so

[tex]\frac{KE2}{KE1} = \frac{A2^2}{A1^2}[/tex]      .............2

[tex]\frac{KE2}{KE1} = \frac{4.7^2}{6.5^2}[/tex]

[tex]\frac{KE2}{KE1}[/tex] = 0.52284

so factor that bug maximum KE change is 0.52284

The factor does the bug's maximum KE change should be considered as the 0.52284.

Since

vertical distance = 6.5 cm

ripples decrease to =  4.7 cm

So here we apply the given formula

KE = (0.5) × m × A² × ω²     .................1

here,

kinetic energy is directly proportional to square of the amplitude.

So,

= 4.7^2/ 6.5^2

= 0.52284

hence, The factor does the bug's maximum KE change should be considered as the 0.52284.

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Answer:

It bends away from the normal

Explanation:

From Snell's law of Refraction, when a ray passes from a medium of lower Refractive index to a medium with higher Refractive index, the Refractive ray will bend towards the normal. However, when the ray passes from a medium of higher Refractive index to a medium of lower Refractive index, the Refractive ray will bend away from the normal.

Now, from the question we are told that Light passes from a material with index of refraction 1.3 into one with index of refraction 1.2.

This means from a higher Refractive index to a lower one and from Snell's law as earlier said, the refracted ray will bend away from the normal

The refracted ray is seen to bend away from the normal.

Let us recall that an optically denser medium will have a higher refractive index. This means that the medium with a refractive index of  1.3  is the denser medium and the medium with a refractive index of  1.2 is the less dense medium.

From the statement in the question, we can boldly say that light is travelling from a denser to less dense medium given the values of the refractive index given. When light is travelling from a denser to a less dense medium, the refracted ray bends away from the normal.

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Answer:

The mas unit is the the 'Kilogram' written as 'kg'

Volume is 10 L

Explanation:

The complete question is

If you have a density of 100 kg/L, and a mass of 1000 units, tell me the following: First, what are the mass units?

Second, what is the volume

mass units is the 'Kilogram', written as 'kg'

density = mass/volume = 100 kg/L

the mass  = 1000 kg

volume = mass/density = 1000/100 = 10 L

Given that,

A charged particle enters a magnetic field with an angle theta .

If [tex]\theta=90^{\circ}[/tex]

We know that,

If the angle is 90° then the charged particle enters perpendicular to the B.

B is magnetic field.

The charged particle will be follow of the circular path.

If the angle is greater than 0 and less than 90° then the charged particle will be show the helical path.

Hence, This is required answer.

Answer:

The magnetic force would be:

[tex]F\approx 2.625\,\,10^{-5}\,\,N[/tex]

Explanation:

Recall that the magnetic force on a charged particle (of charge q) moving with velocity (v) in a magnetic field B, is given by the vector product:

F = q v x B

(where the bold represents vectors)

the vector product involves the sine of the angle ([tex]\theta[/tex]) between the vectors, so we can write the relationship between the magnitudes of these quantities as:

[tex]F=q\,v\,B\,sin(\theta)[/tex]

Therefore replacing the known quantities for the first case:

[tex]F=q\,v\,B\,sin(\theta)\\2.98\,\,10^{-4} \,\,N=q\,(25.7\,\,m/s)\,B\,sin(90^o)\\2.98\,\,10^{-4} \,\,N=q\,(25.7\,\,m/s)\,B\\q\,\,B=\frac{2.98\,\,10^{-4} }{25.7} \,\frac{N\,\,s}{m}[/tex]

Now, for the second case, we can find the force by using this expression for the product of the particle's charge times the magnetic field, and the new velocity and angle:

[tex]F=q\,v\,B\,sin(\theta)\\F=q\,(4.64\,\,m/s)\,B\,sin(29.2^o)\\F=q\,B(4.64\,\,m/s)\,\,sin(29.2^o)\\F=\frac{2.98\,\,10^{-4} }{25.7} \,(4.64\,\,m/s)\,\,sin(29.2^o)\\F\approx 2.625\,\,10^{-5}\,\,N[/tex]

Answer:

[tex]B=2.74\times 10^{-10}\ T[/tex]

Explanation:

It is given that,

A planar electromagnetic wave is propagating in the +x direction.The electric field at a certain point is, E = 0.082 V/m

We need to find the magnetic vector of the wave at the point P at that instant.

The relation between electric field and magnetic field is given by :

[tex]c=\dfrac{E}{B}[/tex]

c is speed of light

B is magnetic field

[tex]B=\dfrac{E}{c}\\\\B=\dfrac{0.082}{3\times 10^8}\\\\B=2.74\times 10^{-10}\ T[/tex]

So, the magnetic vector at point P at that instant is [tex]2.74\times 10^{-10}\ T[/tex].

The magnetic vector of the wave at the point P at that instant is [tex]2.73 \times 10^{-10}T[/tex]

The formula relating electric field and the magnetic field is given as;

[tex]c=\frac{E}{B}[/tex]

From the formula shown:

[tex]B=\frac{E}{c}\\B=\frac{0.082}{3.0\times 10^8}\\B=2.73 \times 10 ^{-10}T[/tex]

Hence the magnetic vector of the wave at the point P at that instant is [tex]2.73 \times 10^{-10}T[/tex]

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Answer:

D) diffraction

Explanation:

Corona is an optical phenomenon produced by the diffraction of sunlight or moonlight, as light moves through water droplets in the atmosphere.

This phenomenon produces one or more diffuse concentric rings of light around the Sun or Moon, usually seen as colored circles.

Therefore, the explanation for these phenomena of colored concentric circles, sometimes seen with the Sun or the Moon involves diffraction.

Answer:

During acceleration, you are moving across a distance over a time, but also increasing how fast we are doing it. Therefore, it means by how many meters per second the velocity changes every second

Explanation:

Answer:

a) for the torque to be maximum, sin should be maximum

i.e (sinФ)maximum = 1

b) therefore the Maximum torque is

Tmax = 0.1838 × 1 = 0.1838  N.m

c) Given the torque is 71.0% of its maximum value; Ф  = 45.24⁰ ≈ 45⁰

Explanation:

Given that; Diameter is 8.40 cm,

Radius (R) = D/2 = 8.40/2 = 4.20 cm = 0.042 m

Number of turns (N) = 17

Current in the loop (I) = 3.20 A

Magnetic field (B) = 0.610 T

Let the angle between the loop's area vector A and the magnetic field B be

Now. the area of the loop is;

A = πR²

A = 3.14 ( 0.042 )²

A =  0.005539 m²

Torque on the loop (t) = NIABsinФ

t = 17 × 3.20 ×0.005539 × 0.610 × sinФ

t = 0.1838sinФ N.m

for the torque to be maximum, sin should be maximum

i.e (sinФ)maximum = 1

therefore the Maximum torque is

Tmax = 0.1838 × 1 = 0.1838  N.m

Given the torque is 71.0% of its maximum value

t = 0.71 × tmax

t = 0.71 × 0.1838

t = 0.1305

Now

0.1305 N.m =  0.1838 sinФ N.m

sinФ = 0.1305 / 0.1838

sinФ = 0.71001

Ф = sin⁻¹ 0.71001

Ф  = 45.24⁰ ≈ 45⁰

Answer:

The intensity at distance 2d from source is  [tex]I_1 = \frac{1}{4} * I[/tex]  

Explanation:

From the question we are told that

     The distance of the wave from point source is  d  

     The  intensity is  [tex]I[/tex]  

     The distance we are considering is  2d

Generally the intensity of a wave is mathematically represented as

            [tex]I = \frac{ P }{\pi d^2 }[/tex]    

Here P is power of point source      

Now when  d =  2d

          [tex]I_1 = \frac{ P }{\pi (2d)^2 }[/tex]        

           [tex]I_1 = \frac{ 1 }{4 } * \frac{ P }{\pi d^2 }[/tex]

    =>   [tex]I_1 = \frac{1}{4} * I[/tex]  

The intensity at a distance 2d from the source is equal to [tex]I'=\frac{I}{4}[/tex]

Given the following data:

To determine the intensity at a distance 2d from the source:

Mathematically, the intensity of a wave is given by the formula:

[tex]I=\frac{P}{\pi d^2}[/tex]

Where:

Since the distance is doubled (2d), we have:

[tex]I'=\frac{P}{\pi (2d)^2}\\\\I'=\frac{P}{4\pi (d)^2}\\\\I'=\frac{1}{4} \times \frac{P}{\pi (d)^2}\\\\I'=\frac{1}{4} \times I\\\\I'=\frac{I}{4}[/tex]

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Answer:

The density is  [tex]\rho_z = 2544 \ kg /m^3[/tex]

Explanation:

From the question we are told that

    The mass of the rock is  [tex]m_r = 1.80 \ kg[/tex]

     The  tension on the string is  [tex]T = 10.8 \ N[/tex]

Generally the weight of the rock is  

        [tex]W = m * g[/tex]

=>     [tex]W = 1.80 * 9.8[/tex]

=>   [tex]W = 17.64 \ N[/tex]

Now the upward force(buoyant force) acting on the rock  is mathematically evaluated as  

        [tex]F_f = W - T[/tex]

substituting values

       [tex]F_f = 17.64 - 10.8[/tex]

      [tex]F_f = 6.84 \ N[/tex]

This buoyant force is mathematically represented as

      [tex]F_f = \rho * g * V[/tex]

Here  [tex]\rho[/tex] is the density of water and it value is [tex]\rho = 1000\ kg/m^3[/tex]

 So

         [tex]V = \frac{F_f}{ \rho * g }[/tex]

        [tex]V = \frac{6.84}{ 1000 * 9.8 }[/tex]

        [tex]V = 0.000698 \ m^3[/tex]

Now for this rock to flow the upward force (buoyant force) must be equal to the length

      [tex]F_f = W[/tex]

      [tex]\rho_z * g * V = W[/tex]

Here z is smallest density of a liquid in which the rock will float

=>     [tex]\rho_z = \frac{W}{ g * V}[/tex]

=>   [tex]\rho_z = \frac{17.64}{ 0.000698 * 9.8}[/tex]

=>   [tex]\rho_z = 2544 \ kg /m^3[/tex]

Answer:

The linear velocity, v = 5.93 m/s

Explanation:

To find the linear velocity after 5 seconds, we find its angular velocity after 5 seconds using

ω' = ω + αt where ω = initial angular speed = 4.00 rev/s = 4.00 × 2π rad/s = 25.13 rad/s, ω' =  = final angular speed, α = angular acceleration = 2.25 rad/s² and t = time = 5.00 s

ω' = ω + αt

= 25.13 rad/s + 2.25 rad/s² × 5.00 s

= 25.13 rad/s + 11.25 rad/s

= 36.38 rad/s

The linear velocity v is gotten from v = rω' where r = radius of pulley = 326 mm/2 = 163 mm = 0.163 m

v = rω'

= 0.163 m × 36.38 rad/s

= 5.93 m/s

So, the linear velocity  v = 5.93 m/s

Answer:

The intensity of sound at rock concert is  10¹⁰ greater than that of a whisper.

Explanation:

The intensity of sound is given by;

[tex]I(dB) = 10Log(\frac{I}{I_o} )[/tex]

where;

I is the intensity of the sound

I₀ is the threshold of sound intensity = 1 x 10⁻¹² W/m²

The intensity of sound at a rock concert

[tex]120 = 10Log(\frac{I}{1*10^{-12}} )\\\\12 = Log(\frac{I}{1*10^{-12}} )\\\\\frac{I}{1*10^{-12}} = 10^{12}\\\\I = 1*10^{-12} *10^{12}\\\\I = 1*10^0\\\\I =1 \ W/m^2[/tex]

The intensity of sound of a whisper

[tex]20 = 10Log(\frac{I}{1*10^{-12}} )\\\\2 = Log(\frac{I}{1*10^{-12}} )\\\\\frac{I}{1*10^{-12}} = 10^{2}\\\\I = 1*10^{-12} *10^{2}\\\\I = 1*10^{-10}\\\\I =10^{-10} \ W/m^2[/tex]

Thus, the intensity of sound at rock concert is  10¹⁰ greater than that of a whisper.

Answer:

potential energy is a stored energy or energy of position (gravitational).

Kinetic energy is a energy of motion.

Explanation:

in the formula K is for the kinetic and the P stand for the potential.

Answer:

1.6×10²⁰

Explanation:

An ampere is a Coulomb per second.

1 A = 1 C / s

The amount of charge after 5 seconds is:

5.0 A × 5 s = 25 C

The number of electrons is:

25 C × (1 electron / 1.6×10⁻¹⁹ C) = 1.6×10²⁰ electrons

Answer:

The wavelength is [tex]\lambda_2 = 534 *10^{-9} \ m[/tex]

Explanation:

From the question we are told that

   The wavelength of the first light is  [tex]\lambda _ 1 = 587 \ nm[/tex]

    The order of the first light that is being considered is  [tex]m_1 = 10[/tex]

     The order of the second light that is being considered is  [tex]m_2 = 11[/tex]

Generally the distance between the fringes for the first light is mathematically represented as

      [tex]y_1 = \frac{ m_1 * \lambda_1 * D}{d}[/tex]

 Here  D is the distance from the screen

 and    d  is the distance of separation of the slit.

      For the second light the distance between the fringes is  mathematically represented as

         [tex]y_2 = \frac{ m_2 * \lambda_2 * D}{d}[/tex]

Now given that both of the light are passed through the same double slit

       [tex]\frac{y_1}{y_2} = \frac{\frac{m_1 * \lambda_1 * D}{d} }{\frac{m_2 * \lambda_2 * D}{d} } = 1[/tex]

=>    [tex]\frac{ m_1 * \lambda _1 }{ m_2 * \lambda_2} = 1[/tex]

=>     [tex]\lambda_2 = \frac{m_1 * \lambda_1}{m_2}[/tex]

=>    [tex]\lambda_2 = \frac{10 * 587 *10^{-9}}{11}[/tex]

=>   [tex]\lambda_2 = 534 *10^{-9} \ m[/tex]

Answer:

total current = 12.417 A

so it will not fuse as current is less than 15 A

Explanation:

given data

toaster = 1140-W

blender = 270-W

lamp = 80-W

voltage = 120 V

solution

we know that current is express as

current = power ÷ voltage   ......................1

here voltage is same in all three device

so

current by toaster is

I = [tex]\frac{1140}{120}[/tex]

I = 9.5 A

and

current by blender

I = [tex]\frac{270}{120}[/tex]

I = 2.25 A

and

current by lamp is

I = [tex]\frac{80}{120}[/tex]

I = 0.667 A

so here device in parallel so

total current is = 9.5 A + 2.25 A + 0.667 A

total current = 12.417 A

so it will not fuse as current is less than 15 A

Answer:

A. 30.38°

B 5.04N

Explanation:

Using

F= ILBsin theta

2 .55N= 8.4Ax 0.5mx 1.2T x sintheta

Theta = 30.38°

B. If theta is 90°

Then

F= 8.4Ax 0.5mx 1.2x sin 90°

F= 5.04N

Answer:

Explanation:

Answer:

Using

A. .E = σ/εo = (q/A)/εo = = q/Aεo so if q = 2q, then

Ef/Ei = 2

B. If L is 2L then Ef = q/4Aεo and

Ef/Ei = 1/4

C. The electric field strength is not effected by d and as long as σ is unchanged, Ef/Ei = 1