The motion of a set of particles moving along the x-axis is governed by the differential equation dx dt = t 3 - x3, where x1t2 denotes the position at time t of the particle. (a) If a particle is located at x = 1 when t = 2, what is its velocity at this time? (b) Show that the acceleration of a particle is

Answer:

Explanation:

Let v₁ and v₂ be velocities at lowest and topmost position . Let r be the radius of the circle .

Let N₁ and N₂ be the normal reaction force .

At the top position

centripetal force = N₂ + mg ;  so

N₂ + mg  = m v₂² / r

At the bottom  position

centripetal force = N₁ - mg ;  so

N₁ - mg  = m v₁² / r

subtracting these two equations

N₁ - mg - N₂ - mg = m v₁² / r  - m v₂² / r

N₁ - N₂ - 2mg = 1/r (m v₁²   - m v₂²  )

N₁ - N₂ - 2mg = 1/r x mg x 2r  ( loss of potential energy = gain of kinetic energy )

N₁ - N₂ =  2mg +  2mg

= 4 mg .

Answer:

The angular acceleration of CD player is [tex]13.93\ rad/s^2[/tex].

Explanation:

Initial angular speed of a CD player is 0 and final angular speed is 41.8 rad/s. Time to change the angular speed is 3 s.

It is required to find the angular acceleration. The change in angular speed of the CD player divided by time taken is called its angular acceleration. It can be given by :

[tex]a=\dfrac{\omega_f-\omega_i}{t}\\\\a=\dfrac{41.8-0}{3}\\\\a=13.94\ rad/s^2[/tex]

So, the angular acceleration of CD player is [tex]13.93\ rad/s^2[/tex].

Answer:147 joules

Explanation:

Mass=m=5kg

Acceleration due to gravity=g=9.8m/s^2

Height=h=3 meter

Potential energy=m x g x h

Potential energy=5 x 9.8 x 3

Potential energy=147 joules

Answer:

K = U ( b )

Explanation:

The expression that describes the kinetic and potential energies at the point mid-way between to the highest and lowest points is  K = U

this is because at the midpoint between the highest point and the lowest point the height is expressed as( h/2) therefore potential energy at that point is expressed as m*g*h/2 therefore the remaining energy at this point will be considered the kinetic energy which will be = m*g*h/2 as well hence at midpoint Kinetic energy = potential energy

Answer:

The electric and magnetic fields gradually increase.

Explanation:

Time constant in RL circuits, denoted by τ, is equal to the value of L / R which is the value of the inductor over the resistor. It is used to calculate the point when the current will reach the maximum value in the steady state of the circuit. Because of this behavior of the circuit, the magnetic field and the electric field gradually increase to their maximum values.

I hope this answer helps.

Answer:

a) 1504.8 J

b) 991.76 J

c) 0J

d) 0J

Explanation:

(a) The work done by the force P on the box is given by the following formula:

[tex]W_P=Px[/tex]

P: applied force = 171N

x: distance in which the for P is applied = 8.80m

you replace the values of P and x and obtain:

[tex]W_P=(171N)(8.80m)=1504.8J[/tex]

(b) The work don by the friction force is:

[tex]W_f=F_fx=\mu N x=\mu Mg x[/tex]

μ = coefficient of kinetic friction = 0.250

M: mass of the box = 46.0kg

g: gravitational constant = 9.8 m/s^2

[tex]W_f=(0.250)(46.0kg)(9.8m/s^2)(8.80m)=991.76J[/tex]

(c) The Normal force is

[tex]N=Mg=(46.0kg)(9,8m/s^2)=450.8N[/tex]

but this force does not do work on the box because the direction is perpendicular to the direction of the force P.

[tex]W_N=0J[/tex]

(d) the same as before:

[tex]W_g=0J[/tex]

Answer:A dielectric material is a material through which virtually no current flows, assuming normally operating voltage

Explanation:

Dielectric materials are ,which means that no current will flow through them, when a voltage is applied

Answer:

t = 2.94 x 10⁶ years

Explanation:

The equation used in the case of constant speed is:

s = vt

t = s/v

where,

s = distance = 12 light years

s = (12 light years)(9.461 x 10¹² km/light year) =  113.532 x 10¹² km

v = speed = 440 km/hr

t = time passed = ?

Therefore,

t = (113.532 x 10¹² km)/(440 km/hr)

t = 2.58 x 10¹¹ hr

Now, converting it to years:

t = (2.58 x 10¹¹ hr)(1 year/8766 hr)

t = 2.94 x 10⁶ years

Answer:

A.

Explanation:

Refraction light rays are bent as they pass into a different medium where its speed is different. As refracted light rays pass from a fast medium to a slow medium, the light ray bends toward the normal to the boundary between the two medium. Light refracts as it travels at an angle into a medium with a different refractive index.

Answer:

a: after 1 seconds it will have fallen 0.2452

after 2 seconds it will have fallen 0.981

after 3 seconds it will have fallen 2.2072

after 4 seconds it will have fallen 3.924

Explanation:

the formula for acceleration due to gravity is (ignoring friction I think)

g = G*M/R^2

earths gravitational constant is about 9.807

g = 9.807*M/R^2

The average weight of a brick is 5 pounds and I'm going to say it's 10 feet off the ground.

g = 9.807*5/10^2.         g = 0.4905 so every second the brick will go 0.4905 fps faster. (fps means feet per second.)

after 1 seconds it will have fallen 0.2452

after 2 seconds it will have fallen 0.981

after 3 seconds it will have fallen 2.2072

after 4 seconds it will have fallen 3.924

Answer: A.

tracking training through a leaming records store LRS.

Explanation:

An LRS uses xAPI to collect learner data, or experiences, from both online and offline sources. These experiences are reported back to the LRS in the form of xAPI statements, where they are stored. These statements can then be retrieved for reporting and interpretation of the learner data.

Given Information:

Power = P = 100 Watts

Voltage = V = 220 Volts

Required Information:

a) Current = I = ?

b) Resistance = R = ?

Answer:

a) Current = I = 0.4545 A

b) Resistance = R = 484 Ω

Explanation:

According to the Ohm’s law, the power dissipated in the light bulb is given by

[tex]P = VI[/tex]

Where V is the voltage across the light bulb, I is the current flowing through the light bulb and P is the power dissipated in the light bulb.

Re-arranging the above equation for current I yields,

[tex]I = \frac{P}{V} \\\\I = \frac{100}{220} \\\\I = 0.4545 \: A \\\\[/tex]

Therefore, 0.4545 A current is flowing through the light bulb.

According to the Ohm’s law, the voltage across the light bulb is given by

[tex]V = IR[/tex]

Where V is the voltage across the light bulb, I is the current flowing through the light bulb and R is the resistance of the light bulb.

Re-arranging the above equation for resistance R yields,

[tex]R = \frac{V}{I} \\\\R = \frac{220}{0.4545} \\\\R = 484 \: \Omega[/tex]

Therefore, the resistance of the bulb is 484 Ω

Answer:

bulb will burn out!

Explanation:

Answer:

The thickness of the door is 0.4230 m

Explanation:

Given;

mass of bullet, m = 0.009 kg

initial velocity of the bullet, u = 803 m/s

final velocity of the bullet, v = 617 m/s

average resistive force of the door on the bullet, F = 5620 N

Apply Newton's second law of motion;

Force exerted by the door on the bullet = Force of the moving bullet

F = ma

where;

F is applied force

m is mass

a is acceleration

Also, Force exerted by the door on the bullet = Force of the moving bullet

[tex]F =ma, \ But \ a =\frac{dv}{dt} = \frac{u-v}{t} \\\\F = \frac{m(u-v)}{t}[/tex]

where;

v is the final velocity of the bullet

u is initial velocity of the bullet

t is time

We need to calculate the time spent by the bullet before it passes through the door.

[tex]t = \frac{m(u-v)}{F} \\\\t = \frac{0.009(803-617)}{5620} = 0.0002979 \ s[/tex]

Distance traveled by the bullet within this time period = thickness of the door

This distance is equivalent to the product of average velocity and time

[tex]S = (\frac{u+v}{2}) t[/tex]

where;

s is the distance traveled

[tex]S = (\frac{u+v}{2}) t\\\\S = (\frac{803+617}{2}) 0.0002979\\\\S = 0.4230 \ m[/tex]

Therefore, the thickness of the door is 0.4230 m

Answer:

Question 3: 2.25 watts

Question 4: 405 joules

Explanation:

question 3:

Current =0.5 amps

Voltage =4.5 volts

Power= current x voltage

Power=0.5 x 4.5

power=2.25 watts

Question 4

Current =0.5 amps

Voltage =4.5v

Time=3 minutes

Time =3x60

Time =180 seconds

Energy=current x voltage x time

Energy =0.5 x 4.5 x 180

Energy =405 joules

Answer: fewer health problems

Explanation:

The benefits of learned optimism that have been found in research are Fewer health problems, Making more money, and a lower divorce rate. The correct option is B.

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In summary, learned optimism has a range of benefits for individuals, including better physical and mental health, greater success in work and education, better relationships with others, and improved resilience. These benefits make learned optimism an important skill for individuals to develop in order to lead happier, healthier, and more successful lives.

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Answer:

a) [tex]\vec{v}_{12}=2.86*10^{8} m/s[/tex]

b) [tex]p=2.81*10^{-16} kg*m/s[/tex]    

Explanation:

a) When we have two particles traveling in parallel directions, the formula for relative velocity is:

[tex]\vec{v}_{12}=\frac{\vec{v}_{1}-\vec{v}_{2}}{1-\frac{\vec{v}_{1}\vec{v}_{2}}{c^{2}}}[/tex]

Here we have that v(1) = -v(2), the speed of the of the second particle is the negative of the first one.

If we use these equivalence we have:

[tex]\vec{v}_{12}=\frac{2\vec{v}_{1}}{1+\frac{\vec{v}_{1}^{2}}{c^{2}}}[/tex]  

[tex]\vec{v}_{12}=\frac{2*2.19*10^{8}}{1+\frac{2.19*10^{16}}{3*10^{16}}}[/tex]  

[tex]\vec{v}_{12}=2.86*10^{8} m/s[/tex]          

And, [tex]\vec{v}_{21}=-2.86*10^{8} m/s[/tex]  

b) The relativistic momentum equation to one particle observed by the other particle, is:

[tex]p=\gamma mv[/tex]

Where gamma is:

[tex]\gamma = \frac{1}{\sqrt{1-\frac{v^{2}}{c^{2}}}}[/tex]

Then gamma will be:

[tex]\gamma=\frac{1}{\sqrt{1-\frac{(2.86*10^{8})^{2}}{(3*10^{8})^{2}}}}[/tex]

[tex]\gamma=3.31[/tex]

Finally, the value of the momentum will be:

[tex]p=3.31*2.97*10^{-25}*2.86*10^{8}[/tex]    

[tex]p=2.81*10^{-16} kg*m/s[/tex]    

I hope it helps you!                        

Answer:

v_max = (1/6)e^-1 a

Explanation:

You have the following equation for the instantaneous speed of a particle:

[tex]v(t)=ate^{-6t}[/tex]   (1)

To find the expression for the maximum speed in terms of the acceleration "a", you first derivative v(t) respect to time t:

[tex]\frac{dv(t)}{dt}=\frac{d}{dt}[ate^{-6t}]=a[(1)e^{-6t}+t(e^{-6t}(-6))][/tex]  (2)

where you have use the derivative of a product.

Next, you equal the expression (2) to zero in order to calculate t:

[tex]a[(1)e^{-6t}-6te^{-6t}]=0\\\\1-6t=0\\\\t=\frac{1}{6}[/tex]

For t = 1/6 you obtain the maximum speed.

Then, you replace that value of t in the expression (1):

[tex]v_{max}=a(\frac{1}{6})e^{-6(\frac{1}{6})}=\frac{e^{-1}}{6}a[/tex]

hence, the maximum speed is v_max = ((1/6)e^-1)a

Answer is Weaker. If it is talking about the objects' gravitational forces.

Answer:

Total internal reflection (TIR) is the phenomenon that involves the reflection of all the incident light off the boundary. TIR only takes place when both of the following two conditions are met: the light is in the more dense medium and approaching the less dense medium.

Explanation: Hope i helped!!!

Answer:

A.  falling water

Explanation:

I got it right on Edgenuity. Good luck on your quiz.

In hydroelectric plants, water falls on turbine and makes it rotate. In generator, this mechanical energy transforms into electrical energy.

Hydroelectric power is generated by turbines that turn the potential energy of falling or swiftly flowing water into mechanical energy, which is then used to power generators. The most popular renewable energy source in the early 21st century was hydroelectricity, which in 2019 accounted for more than 18% of the world's total power producing capacity.

Water is gathered or stored at a higher elevation during the production of hydroelectric power and then transported through substantial pipes or tunnels (penstocks) to a lower elevation; the difference between these two elevations is referred to as the head. The falling water turns turbines as it nears the bottom of the pipelines. In turn, the turbines power generators, which transfer the mechanical energy of the turbines into electricity.

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Answer:

Explanation:

frequency n = 90 x 10⁶ Hz .

time period T = 1 / n

= 1 / 90 x 10⁶

= 1.11 x 10⁻⁸ S.

wavelength = velocity of light / frequency

= 3 x 10⁸ / 90 x 10⁶

= 3.33 m

maximum value of the magnetic field. ( B₀ )

E₀ / B₀ = c where E₀ and  B₀ are maximum electric and magnetic field .

E₀ / c=  B₀

200/ 3 x 10⁸

= 66.67 x 10⁻⁸ T .

expressions in SI units for the space and time variations of the electric field

[tex]E=E_{0y}sin(2\pi nt - \frac{2\pi x}{\lambda} )[/tex]

[tex]E=200sin(180\times 10^6\pi t - \frac{2\pi x}{\lambda} )[/tex] N/C

[tex]B=B_{0z}sin(2\pi nt - \frac{2\pi x}{\lambda} )[/tex]

[tex]B=66.67\times 10^{-8}sin(180\times 10^6\pi t - \frac{2\pi x}{\lambda} )[/tex] T

Answer:

The acceleration is  [tex]a = 2.5 \ m/s^2[/tex]

Explanation:

From the question we are told that

   The mass of the metal block is [tex]m_b = 2 \ kg[/tex]

    The mass flow rate of the water is  [tex]\r m = 1\ kg/s[/tex]

    The speed of the water of the water release is [tex]v_w = 5 m/s[/tex]

Generally according to the law of conservation of linear momentum

    [tex]p_i = p_f[/tex]

Now  [tex]p_i[/tex] is the initial momentum of the system which mathematically represented as

       [tex]p_i = m_w * v_w + m_b * v_b[/tex]

Now [tex]m_w[/tex] is the mass of water at the point of contact with the block which can be deduced as [tex]m_w = 1 \ kg[/tex]

Now since at initial the block is at rest

       [tex]v_b = 0 \ m/s[/tex]

So

      [tex]p_i = 1 * 5[/tex]

     [tex]p_i = 5 \ kgm/ s[/tex]

And  [tex]p_f[/tex] is the final  momentum of the system which mathematically represented as

     [tex]p_f = m_w * v__{fw} } + m_b * v__{fb}}[/tex]

So   [tex]v__{fw} }[/tex] is the final velocity of water which is zero due to the fact that when the water hits the block it losses its momentum and eventually the velocity becomes zero

    So

          [tex]5 = 2 * v__{fb }[/tex]

Thus  [tex]v__{fb }} = \frac{5}{2}[/tex]

        [tex]v__{fb }} = 2.5 \ m/s[/tex]

Thus  

       [tex]p_f = 2.5 * 2[/tex]

      [tex]p_f = 5 \ kgm /s[/tex]

Now the average momentum change is  

        [tex]p_a = \frac{p_i +p_f}{2}[/tex]

       [tex]p_a = \frac{5+5}{2}[/tex]

        [tex]p_a =5 kgm/s[/tex]

Now the force acting on the block is  

      [tex]F = \frac{p_a }{t}[/tex]

and from the question the initial movement of the block took 1s as it is a mass of water moving at a rate of 1kg/s that caused the first movement of the block

  So

        [tex]F= \frac{5}{1}[/tex]

       [tex]F= 5 \ N[/tex]

Now the acceleration is  

       [tex]a = \frac{F}{m_b}[/tex]

=>     [tex]a = \frac{5}{2}[/tex]

        [tex]a = 2.5 \ m/s^2[/tex]

Answer:

The center of mass move with the velocity of -3.487 m/s.

Explanation:

Given values of block A.

Mass of block A, (M1) = 4 kg

Speed of block A, (V1) = 2 m/s

Given values of block B.

 Mass of block B, (M2) = 8.4 kg

Speed of block B, (V2) = -6.1 m/s

Below is the formula to find the velocity of center of mass.

[tex]Velocity = \frac{M1V1 + M2V2}{M1 + M2} \\[/tex]

[tex]= \frac{4 \times 2 + 8.4 \times (-6.1) }{4 + 8.4} \\[/tex]

[tex]= \frac{- 43.24}{12.4}\\[/tex]

[tex]= - 3.487 m/s[/tex]

Answer:

26.92 N

Explanation:

The normal reaction of the ball is due to two force component acting on it.

However ; the acceleration is in polar coordinate which is given by the relation:

[tex]a^ { ^ \to} = (r- r \omega^2) \hat {e_r} + ( r \theta + 2 r \omega ) \hat {e_ \theta}[/tex]

[tex]a_{\theta} = r \theta + 2 r \omega[/tex]

Given that :

ω = 5 rad/s

mass m = 6 kg

θ = 30 ◦

r = 0.9 m

speed v =  0.4 m/s

[tex]a_{\theta} = 0 + 2(-0.4)*5[/tex]

[tex]a_{\theta}= -4 \ m/s[/tex]

The normal force reaction (N) that the arm applies to the ball at this instant is :

N = mg cos θ  + [tex]ma_{\theta}[/tex]

N = (6 × 9.8× cos 30) + (6 ×(-4))

N = 26.92 N

Complete Question

The complete question is shown on the first uploaded image

Answer:

Explanation:

From the question we are told that

     The mass of the bat is [tex]m_b = 0.800 \ kg[/tex]

      The bat length is  [tex]L_b = 0.900 \ m[/tex]

      The distance of the bat's center of mass to the handle end is  [tex]z_c = 0.600 \ m[/tex]

      The moment of inertia of the bat is    [tex]I = 0.0530 \ kg \cdot m^2[/tex]

The objective of the solution is to find  x   which is the distance from the handle of the bat to the point where the baseball hit the bat

Generally the velocity change at the end of the bat is mathematically represented as

         [tex]\Delta v_e = \Delta v_c - \Delta w* z_c[/tex]

         Where  [tex]\Delta v_c[/tex] is the velocity change at the center of the bat  which is mathematically represented as

                [tex]\Delta v_c = \frac{Impulse}{m_b }[/tex]

We are told that the impulse is  J so

              [tex]\Delta v_c = \frac{J}{m_b }[/tex]

And   [tex]\Delta w[/tex] is the change in angular velocity which is mathematically represented as

         [tex]\Delta w = \frac{J (z -z_c)}{I}[/tex]

Now we have that

           [tex]\Delta v_e = \frac{J}{m_b } - [\frac{J (x- z_c)}{I} ] * z_c[/tex]

Before a swing when the bat is at rest the velocity change a the end of the bat handle is zero  and the impulse will be  1

   So  

            [tex]0 = \frac{1}{m_b } - [\frac{J (x- z_c)}{I} ] * z_c[/tex]

=>           [tex]x = \frac{I}{m_b z_c} + m_b[/tex]

substituting values

            [tex]x = \frac{0.530}{0.800 * 0.600} + 0.600[/tex]

           [tex]x = 0.710 \ m[/tex]

Answer:

coefficient of friction (μ) and normal force (N)

Answer: How hard the surfaces push together and the types of surfaces involved

Explanation:

Answer:171 N

Explanation:

Answer:

171 N.

Explanation:

Answer:

the answer is a

Explanation:

Answer:

The force needed is the weight of the rock minus the buoyant force.

Explanation: