You can buy 50 rolls of toilet paper for $12.50. Write a ratio showing the unit rate of rolls per $1.

The line on the speed-time  graph will slant from up to down showing a state of coming to rest.

What is speed - versus - time graph?

A speed versus-time-graph is a type of graph that shows the relationship between the speed of an object and the time of motion of the object.

For upward acceleration of an object when the object is speeding up, the line on the graph for such motion increases upward in a direct relationship with time of motion.

For a downward motion in which the object in motion slows down, the line on the graph for such motion will slant downward showing a gradual decrease in the speed of the object.

Thus, for a car that is driving away from you at a constant speed for a while, and then it gradually slows to a stop, the line on the speed-time  graph will slant from up to down showing a state of coming to rest.

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Takeoff speed of the froghopper is 2.786 m/s

By analyzing the vertical motion of the froghopper,

The initial vertical velocity of the froghopper as it jumps from the ground is given by

[tex]U_{y}[/tex] = U₀Sinθ

here, θ = 57°

Therefore Sin57° = 0.838

[tex]U_{y}[/tex]= 0.838U₀

Vertical motion is the motion that occurs when the object is thrown all the way up, i.e. , the initial velocity or force acts only in the vertical axis, therefore this motion has only vertical motion.

Maximum height reached by the froghopper is h = 278 mm

h = 0.278 m

As we know that vertical velocity at the point of maximum height will be zero,

[tex]V_{y} = 0[/tex]

Since the vertical motion is an accelerated motion with constant (de)acceleration, so by using Equation of motion,

[tex]V^{2} _{y} - U^{2} _{y} = 2gh[/tex]

[tex]U_y = \sqrt{V^{2} _{y} - 2gh }[/tex]

[tex]U_y = \sqrt{0 - 2(-9.81) (0.278) }[/tex]

[tex]U_{y}[/tex] = 2.335 m/s

[tex]U_{y}[/tex] = 0.838U₀

U₀ = [tex]\frac{U_y}{0.838}[/tex]

U₀ = [tex]\frac{2.335}{0.838}[/tex]

U₀ = 2.786 m/s

The takeoff speed of the froghopper is 2.786 m/s.

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Features that must be present for a stable well-designed racing car.

For, a racing car the speed is high and also to finish the race, the car should be easy to turn around.

Lower the centre of gravity more will be its stability.

A low centre of gravity is a must for a stable well-designed racing car.

The auricle, also known as pinna is the visible portion of outer ear.

The purpose of auricle is to collect sound waves and send them through ear canal.

The eustachian tube connecting middle ear and back of nose, equalizes air pressure on both sides of the eardrum.

Thus, the statement is false.

The magnitude of the force is found to be 274.19N.

Force (F1)acting on θ1(190°) is 180N

Force (F2)acting on θ2(260°) is 140N

Therefore the angle between F1 and F2 is

θ2-θ1 = 180°-140° =40°

Now we calculate magnitude of force,

Magnitude of force ,F= F1+F2

F. F = [tex]\sqrt{ ( F1+F2). (F1+F2) }[/tex]

|F|² = [tex]\sqrt{F1 ²+F2 ²+F1 F2 COS θ}[/tex]

F= [tex]\sqrt{ 180²+140²+2×180×140× cos40°}[/tex]

F= [tex]\sqrt{32400+19600+23184}[/tex]

F= [tex]\sqrt{75184}[/tex]

F= 274.19N.

Thus, the magnitude of the force is found to be 274.19N.

The magnitude of the force is the entire quantity of forces acting on an object. When all forces are pulling in the same direction, the force becomes stronger. The strength of a force decreases as it is applied to an object from various angles.

Force has a magnitude and a direction, thus a vector quantity. The outcomes of two equal-sized forces acting in opposite directions one in the east and the other in the west are not the same.

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The gauge pressure at the bottom of the tank is 297500 N/m².

The magnitude of the net force that acts on a square access hatch at the bottom of the tank is 107100 N.

The pressure at the bottom of the tank is the pressure due to the weight of the fluid above it and the atmospheric pressure.

The pressure due to the atmosphere = 101300 N/m²

The pressure due to the water above the tank is calculated with the formula below:

Pressure = height * density * g

height of tank = 20 m

the density of water = 1 * 10³ kg/m³

g = 9.81 m/s²

Pressure due to water = 20 * 1 * 10³ kg/m³ * 9.81

Pressure due to water = 192000 N/m²

Total pressure = 192000 + 101300 N/m²

Total pressure = 297500 N/m²

B. Force = pressure * area

area of the hatch = 0.6 * 0.6 = 0.36 m²

Force = 297500 N/m² * 0.36 m²

Force = 107100 N

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Given data:

* The extension of the steel wire is 0.3 mm.

* The length of the wire is 4 m.

* The area of cross section of wire is,

* The young modulus of the steel is,

Solution:

The young modulus of the steel in terms of the force and extension is,

where F is the force acting on the steel wire,, l is the original length of the wire, dl is the extension of the wire, and A is the area,

Substituting the known values,

Thus, the force which produce the extension of 0.3 mm of the steel wire is 31.5 N.

The mass M₂ that one must hang from the glider in order to obtain an acceleration equal to that of the Porsche is 0.664 kilograms.

The initial velocity U of the porche is 0miles/hours or 0m/s.

The final velocity V of the porche is 60miles/hours or 26.84 m/s.

Total time period is 5 seconds,

Using equation of motion,

V+U = at

Putting all the values,

26.84= a(5)

a =  5.364 m/s².

Now, the mass of the glider is 0.550 Kg.

Let us assume that the glider and the mass are connected by a string. The tension in the string is T.

The mass M2 is hanged from one end the glider is on the horizontal surface.

When the system is released,

Total force on glider,

(0.550)a = T

Total force on the mass M2,

M2(a) = M2g - T.

Putting the value of T,

M2a = M2g - (0.550)a

(0.550)a = M2(g-a)

M2 = (0.550)×5.364/(9.8-5.364)

M2 = 0.664 Kg.

The required mass to be hung is 0.664 Kg.

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Answer:

Approximately [tex]7.1\; {\rm kN}[/tex] ([tex]5 \sqrt{2}\; {\rm kN}[/tex].)

Explanation:

Let [tex]F_{1}[/tex] and [tex]F_{2}[/tex] denote the two forces that act on this beam. Let [tex]s_{1}[/tex], [tex]s_{2}[/tex], [tex]\theta_{1}[/tex], and [tex]\theta_{2}[/tex] denote the distance from pivot and angle relative to the beam of the two forces, respectively. The magnitude of the torques that the two forces exert on this beam will be [tex]F_{1}\, s_{1}\, \sin(\theta_{1})[/tex] and [tex]F_{2}\, s_{2}\, \sin(\theta_{2})[/tex], respectively.

The two forces in this question act on the beam from opposite sides of the pivot. Hence, for the beam to be in equilibrium, the torque from the two forces need to be equal in magnitude. In other words:

[tex]F_{1}\, s_{1}\, \sin(\theta_{1}) = F_{2}\, s_{2}\, \sin(\theta_{2})[/tex].

Let [tex]F_{1}[/tex] denote the [tex]5\; {\rm kN}[/tex] force that the load exerts on this beam; [tex]\theta = 90^{\circ}[/tex] since this load is placed directly on the beam. The normal force from the load will be perpendicular to the beam.

Let [tex]F_{2}[/tex] denote the force that the rope exerts on this beam; [tex]\theta = 45^{\circ}[/tex].

Note that [tex]s_{1} = s_{2}[/tex] since the pivot is exactly halfway between the two forces.

Rearrange the equation [tex]F_{1}\, s_{1}\, \sin(\theta_{1}) = F_{2}\, s_{2}\, \sin(\theta_{2})[/tex] to find the unknown [tex]F_{2}[/tex]:

[tex]\begin{aligned}F_{2} &= \frac{F_{1}\, s_{1}\, \sin(\theta_{1})}{s_{2}\, \sin(\theta_{2})} \\ &= \frac{F_{1}\, \sin(\theta_{1})}{\sin(\theta_{2})} && (\text{since $s_{1} = s_{2}$}) \\ &= \frac{5\; {\rm kN}\, \sin(90^{\circ})}{\sin(45^{\circ})} \\ &= \frac{5\; {\rm kN}}{(1 / \sqrt{2})} \\ &= 5 \sqrt{2}\; {\rm kN} \\ &\approx 7.1\; {\rm kN} \end{aligned}[/tex].

The tension in the rope will be equal in magnitude to the force exerted on the beam: approximately [tex]7.1\; {\rm kN}[/tex] ([tex]5 \sqrt{2}\; {\rm kN}[/tex].)

The penny will roll past Position 1 since energy cannot be created or destroyed, therefore the correct answer is option B.

The sum of all the energy in motion (total kinetic energy) and all the energy that is stored in the system (total potential energy) is known as mechanical energy.

ME= PE + KE

As given in the problem if a penny, starting from rest at Position 1, rolls down and then up a curved track towards Position 5.

When it reaches Position 5, it rolls back down the track, then we have to find out  Which description below is most consistent with what you can expect from the penny's motion,

Thus, the penny will roll past Position 1 since energy cannot be created or destroyed, therefore the correct answer is option B.

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If an average laser pulse power is 74 kW, and contains 1 mJ of light energy, each laser pulse lasts for a time period of 0.074 ns

E = P t

E = Light energy

P = Pulse power

t = Time

E = 74 KW = 74 * 10³ W

P = 1 * [tex]10^{-3}[/tex] J

t = E / P

t = 74 * 10³ / 1 * [tex]10^{-3}[/tex]

t = 74 * [tex]10^{6}[/tex] s

t = 0.074 ns

Power is the rate of work done. It can also be called as rate at which energy is used. This can be used to all forms of work and all types of energy.

Therefore, each laser pulse lasts 0.074 nanosecond.

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Answer:

1.332 N

Explanation:

Net Force = Mass x Acceleration
1.2 x 1.11 = 1.332 N

I'm so sorry if I'm wrong.

In order to calculate the time needed, let's use the formula below:

Where P is the power in Watts, E is the energy/work in Joules and t is the time in seconds.

First, let's convert the energy from kJ to J (1 kJ = 1000 J):

So, for P = 400, we have:

Therefore the time needed is 750 seconds.

a) Frequency is the number of complete oscillations per second. Looking at the graph, there are 9 complete oscillations in 5 seconds. Thus,

Frequency = 9/5 = 1.8 oscillations per second

Frequency = 1.8 Hz

Period = 1/frequency = 1/1.8

Period = 0.056 s

b) When we differenctiate displacement with respect to time, the result is velocity.

Recall, period = 1/f = 5/9 cycles

1/4 cycle behind = 1/4 x 5/9 = 5/36

It is delayed with 5/36 sec with respect to displacement.

5/36 sec = 0.139 sec

Acceleration = first derivative of velocity = second derivative of displacement = 1/4 cycle behind velocity = 1/2 cycle behind displacement =

5/36 = 0.139 sec delayed with respect to velocity

= 5/18 = 0.2777 secs delayed with respect to displacement

Thus, the number of seconds out of phase with the displacements is 0.278 seconds

c) The formula for calculating the period of an ideal pendulum anywhere is

T = 2π√length/local gravity). We would calculate the local gravity.

From the information given,

length = 0.2

T = P = 5/9

Thus,

5/9 = 2π√0.2/local gravity)

(5/9)/2π = √0.2/local gravity

Square both sides. It becomes

[(5/9)/2π]^2 = 0.2/local gravity

local gravity = 0.2/[(5/9)/2π]^2

local gravity = 25.56 m/s^2

Thus,

acceleration due to gravity = 25.56 m/s^2

Recall, earth's gravity = 9.8 m/s^2

number of g forces = 25.56/9.8

number of g forces = 2.61

B: The change in temperature increases the force of the collisions of

the container and gas particles, so the pressure increases.

P = F/A

Force is directly proportional to Force, so , if force increases also Pressure.

Thesppeed of electromagnetic waves remains the same an is eqal to the speed of light. The wavelength is rearlated tothe energy bty the following ormula:

Wher:

Therefore, if the wavelength increases the frequency must decrease.-

Since the energy is proportiona to the frequency if the dfrequency decreases the energy decreases. Therefore, the right answer is A.

Answer:

energy decreases

Explanation:

hope this helps!

Mayflower Compact influenced the colonists to believe that all citizens would have to abide by the new laws created

The colonists who sailed for the New World created a set of self-government laws known as the Mayflower Compact. The Pilgrims and other immigrants hoped to settle in northern Virginia as soon as they arrived in America. The immigrants' ship was forced off track by perilous shoals and storms and instead came ashore in Massachusetts, close to Cape Cod, outside of Virginia's authority.

The colonial authorities knew that life without laws may be devastating, so they created the Mayflower Compact to assure that a workable social structure would prevail. It preserved the idea of a law enacted by the people. This is the essential tenet of democracy. The Declaration of Independence was influenced by the notion that all citizens, not just a small group of elites, should have their interests represented by the government.

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Given:

The depth of the stream, d=30 cm

The refractive index of water, n=1.33

To find:

The apparent depth of the stream.

Explanation:

Let the eye of the fisherman is at a large height from the surface of the water.

Thus,

Where i is the angle of incidence and r is the opposite side of the angle of incidence.

And,

Where r is the angle of refraction and h is the apparent depth of the stream.

The refractive index of the air is n_a=1.

From snell's law,

On substituting the known values,

Final answer:

The correct answer is option d.

Given,

The mass of the object, m=2 kg

The applied force, F=15 N

The frictional force, f=5 N

The frictional force is a force that opposes the motion of an object. Hence it will be always be directed opposite to the direction of motion of the object.

The net force acting on the object is given by,

From Newton's second law of motion, the net force is given by,

Where a is the acceleration of the object.

Therefore,

On substituting the known values,

Therefore the acceleration of the object is 5 m/s²

Answer:

The answer of the question is nebular theory

From the calculations, the normal force on the body is 345 N.

Let us recall the theory of Newton that states that action and reaction are equal and opposite. We know that the force that is exerted on an object is equal to the reaction of that surface of the object on the source of the force.

We know that the normal force can be given by the formula;

N = mgcosθ

m = mass of the object

g = acceleration due to gravity

θ = angle involved

We would now have

N = 43.0 kg * 9.8 m/s^2 * cos 35

N = 345 N

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Answer:

d = rt

Explanation:

distance = ?

rate = 18 m/s

time = 42 x 60 = 2520 s

distance = 18 x 2520 = 45360 m

a) Peak value = 20

b) Average value = 9.0

c) RMS value = 14.15

The peak-to-peak value = 40

c) The rms value

b) Average value over alternation of the sine wave

Answer:

For parallel plate capacitor ,the capacitance C=dAϵ0

Area, A=ϵ0Cd=8.85×10−121×10−3=1.13×108m2

Pls Check This Answer Is correct or not

actually i am not sure

Jack speed as he hits the water is 14.13m/s

What is speed?
The speed of an object, also known as v in kinematics, is the size of the change in that object's position over time or the size of the change in that object's position per unit of time, making it a scalar quantity. The instantaneous speed is the upper limit of the average speed as the duration of the time interval approaches zero. The average speed of an item in a period of time is equal to the distance travelled by the object divided by the duration of the period. Velocity and speed are not the same thing.

The only force on Jack is gravity, which points straight down, and has an acceleration of 9.91m/s².  Whether he's falling off a bridge or simply standing still on the surface of the earth, the acceleration due to gravity is the same.

If you're looking for the speed of Jack as he hits the water, you just need to solve for v in the equation[tex]$v^2 = v_0^2 + 2ad$[/tex].  
Here,
v is Jack's speed as he hits the water,
[tex]$v_0$[/tex] is Jack's initial speed (which is zero since he's not moving when he jumps),
a is Jack's acceleration (which is 9.91m/s²), and
d is Jack's displacement (which is the height of the bridge, which you said is 10m).  
This gives you an answer of [tex]$v = \sqrt{2ad} = \sqrt{2(9.91)(10)} = 14.13 \ \mathrm{m/s}$[/tex]

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Answer: Cs = [m1c1(T - T1) + mcCc(T - Ts)]/Ms(Ts - T)

Explanation:

The concept of heat exchange which is expressed as

heat lost by a hot body = heat gained by a cold body

The specific heat of a solid substance as determined by the method of mixture using the heat exchange concept would be

Heat lost by substance = heat gained by liquid + heat gained by calorimeter

Thus,

MsCs(Ts - T) = m1c1(T - T1) + mcCc(T - Tc)

Dividing both sides by Ms(Ts - T)

The formula for calculating the specific heat capacity by method of mixtures is

Cs = [m1c1(T - T1) + mcCc(T - Ts)]/Ms(Ts - T)

Where

m1 = mass of liquid

c1 = specific heat of liquid

ms = mass of substance

Cs =specific heat of substance

mc = mass of calorimeter

Cc = specific heat of material used in making the calorimeter

T = Final temperature of the mixture

T1 = initial temperature of the liquid

Ts = initial temperature of the substance

The acceleration of a car, moving along a straight line, that increases its velocity from 0 to 15 is A=1.5m/s.

Acceleration = Velocity Change / Time Interval

So,

A=15/10

A=1.5m/s .

A slowing car slows down. It also accelerates because the speed changes. Imagine a car driving down the street. As speed increases, the car has positive acceleration. When a car turns a corner at a constant speed it changes direction and thus accelerates. The faster the rotation the greater the acceleration.

Therefore, any change in velocity in magnitude and direction causes acceleration. The main causes of poor acceleration are air and fuel issues and sensor issues. However mechanical problems can also cause poor performance. The car is moving forward and accelerating in the positive direction so the acceleration is in the same direction as the car is moving. An object can also have positive acceleration if it slows down while moving in a negative direction.

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The current density of a 7.0 mm diameter copper wire that carries a current of 7.0 μA is 18.19 × 10⁻³ A/m².

The quantity of electric modern-day journeying in step with the unit move-phase region is known as current density and is expressed in amperes per rectangular meter. The more present-day a conductor, the higher could be the modern-day density. current density is the quantity of electrical modern flowing in step with the unit move-sectional region of a material.

subsequently, the SI unit of current density needs to be Ampere/meter2. Ohm's law relates the current flowing via a conductor to the voltage V and resistance R; this is, V = IR. An alternative assertion of Ohm's law is I = V/R.

current I = 0.7 μA

r = 3.5mm

J = I/A = I/πr³

J = 0.7 × 10⁻⁶ / 3.14 × (3.5 × 10⁻³)²

J = 18.19 × 10⁻³ A/m²

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A cylinder with a movable piston contains 3 moles of hydrogen at standard temperature and pressure. The walls of the cylinder are made of a heat insulator, and the piston is insulated by having a pile of sand on it. By what factor does the pressure of the gas increase if the gas is compressed to half its original volume?

Solution :

The cylinder is completely insulated from its surroundings. As a result, no heat is exchanged between the system (cylinder) and its surroundings. Thus, the process is adiabatic.

Initial pressure inside the cylinder =P1

Final pressure inside the cylinder =P2

Initial volume inside the cylinder =V1

Final volume inside the cylinder =V2

Ratio of specific heats, γ=CVCP=1.4

For an adiabatic process, we have:

P1V1γ=P2V2γ

The final volume is compressed to half of its initial volume.

∴V2=V1/2

P1V1γ=P2(V1/2)γ

P2/P1=V1γ/(V1/2)γ

=21.4=2.639

Hence, the pressure increases by a factor of 2.639.

Answer:

The cylinder is fully isolated from the rest of the environment.

There is no heat exchange between the system (cylinder) and its surroundings as a result of the design. As a result, the process is called adiabatic.

P1 represents the initial pressure inside the cylinder.

P2 is the final pressure within the cylinder.

V1 is the volume of the cylinder at its beginning.

The final volume of the cylinder is equal to V2.

The specific heat ratio, = Cp / Cv = 1.4,

We have the following for an adiabatic process:

P1V1γ = P2V2γ

After compression, the final volume is reduced to half of its original size.

Hence,

V2 = V1 / 2

P1V1γ = P2(V1 / 2)γ

P2 / P1 = V1γ / (V1 / 2)γ

= 21.4

We get,

= 2.639

Therefore, the pressure increases by a factor of 2.639

Explanation:

hope it helps you

The statement that correctly differentiates between astronomy and cosmology is as follows: Astronomy is a much broader study of the universe as a whole, while cosmology is a more focused study on specific objects or celestial bodies contained within the universe (option A).

Astronomy is the study of the physical universe beyond the Earth's atmosphere, including the process of mapping locations and properties of the matter and radiation in the universe.

On the other hand, cosmology is the study of the physical universe, its structure, dynamics, origin and evolution, and fate.

Astronomy studies objects and phenomena beyond Earth, whereas cosmology is a branch of astronomy that studies the origin of the universe and how it has evolved.

Therefore, it can be said that astronomy studies the universe from a much broader sense while cosmology is much more specific study.

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