alice prevents on object from intersecting with another object. that is two objects cannot occupy the same space. true or false
All matter has volume but also impenetrability because it occupies space, and two objects cannot occupy a same space at the same time.
What matters is this?An object that occupies space and has inertia is said to be matter, which is composed of numerous types of particles. The different kinds of particles each get a unique mass and size, according to the fundamentals of current physics. The electron, proton, and neutron are three of the most prevalent instances of material particles.
What are matter's characteristics, exactly?Anything with mass and physical space is considered matter. Matter underlies everything that you can see and touch. The three primary types of matter are gases, liquids, and solids. It also possesses qualities that can be expressed through conductivity, magnetism, solubility, density, etc.
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For a 500 gram ball traveling around a 40 cm diameter circle, calculate the angular speed of the ball if it takes 0.5 seconds to make one complete revolution. A. 1.6 π rad/s B, 0.4 π rad/s C. 4 π radis
The angular speed of the ball if it takes 0.5 seconds to make one complete revolution, is Option C. 4 π radius.
Angular speed is the velocity of the object in rotational motion. Distance traveled is represented as θ and is measured in radians. The time taken is measured in terms of seconds. therefore, the angular velocity is articulated in radians consistent with seconds or rad/s.
Angular velocity or rotational velocity, additionally called angular frequency vector, is a pseudovector illustration of how rapidly the angular function or orientation of an item modifications with time.
Calculation:-
The angluar speed ω = ΔΕ/ΔT
= (2π - 0)/0.5
= 4π radis
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Two rods are made of the same kind of steel and have the same diameter. A force of magnitude F is applied to each end of each rod. Compared to the rod of length L, the rod of length 2L has
Compared to the rod of length L, the rod of length 2L has The same stress and same strain.
Since we know that Tensile Stress is determined by the relation :
Tensile Stress = [tex]\frac{F}{A}[/tex]
Where F is the force applied and A is the circular area, which will definitely remain same for both of the rods as they have same diameter.
aslo the Tensile Strain, which is dependent on the young's modulus and stress which would remain same for both of the rods as the material used is same and the stress is alo the same.
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the water used in many sprinkler systems is recycled. for instance, a single water particle in a sprinkler system travels 85 m and then returns to the same point. what is the displacement of this water particle during one cycle?
The displacement is zero since a single water particle in a sprinkler system travels 85 m and then returns to the same point. Recycling has long been acknowledged as a useful strategy.
There isn't a limitless supply of clean drinking water where we live. We must make the most of it, and part of that means reusing our water in ways that keep it clean for drinking. On-site water can be recycled and reused.
d= 0
because initial and final points are same. therfore, the displacement covered is zero.
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The larger the frequency of a photon of light, the _______ the energy of the photon.
The larger the frequency of a photon of light, the lower the energy of the photon.
The energy of a photon is proportional to its electromagnetic frequency. The energy of a photon depends on its wavelength in such a way that its energy is inversely proportional to its wavelength. The higher the frequency of photon energy, the greater its energy.
The energy carried by a single photon is referred to as photon energy. The amount of energy is proportional to the electromagnetic frequency of the photon and thus inversely proportional to the wavelength. The higher the frequency of a photon, the greater its energy. The longer the wavelength of a photon, the lower its energy. Frequency is defined as the number of complete wavelengths in a given unit of time. The frequency and energy (E) of a wavelength decrease as its size increases.
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28. Ratman's rat mobile is traveling at 80m/s North when it turns on its rocket boosters
accelerating the rat mobile to 200 m/s in 4 seconds.
What's the rat mobiles acceleration?
The acceleration of rate mobile is 30 m/s².
Given - Initial velocity=80m/s , Final Velocity=200m/s , time= 4sec
To find out acceleration.
Principle- Acceleration means rate of change of velocity. Mathematically derivative of velocity with the function of time is acceleration.
a=dv/dt
a=(vₙ-v )/dt
substitute vₙ=200m/s , v=80m/s , dt=4sec
a= [ 200 -80 ]/4
a= 120/4
acceleration ⇒ a=30 m/s²
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The reason that most seti programs choose to listen at microwave radio frequencies is that.
The reason that most SETI programs choose to listen at microwave radio frequencies is that sending information is via microwaves is the most efficient way.
What is a microwave?Microwave radiation has wavelengths between one metre and one millimeter, which correspond to frequencies between 300 MHz and 300 GHz, respectively.
What is a radio frequency?In the frequency range between about 20 kHz and about 300 GHz, radio frequency is the rate at which an alternating electric current or voltage, a magnetic, electric, or electromagnetic field, or a mechanical system, oscillates.
The most energy-efficient method of sending information is via microwaves. Because of this, the majority of SETI programmes opt to listen at microwave radio frequencies.
Hence , the reason that most SETI programs choose to listen at microwave radio frequencies is that sending information is via microwaves is the most efficient way.
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for two objects in space with very different masses, the gravitational force causes:
A.
the two objects to remain stationary.
B.
the less-massive object to orbit the more-massive object.
C.
the more-massive object to orbit the less-massive object.
D.
the two objects to both orbit a central point together.
A solar-powered car has a kinetic energy of 110250 J. Its mass is 180 kg. Work out how fast the car is travelling
Answer:
Speed = 126 km/h
Explanation:
Given:
Wk = 110250 J - Kinetic energy of the car
m = 180 kg - Mass
________________
V - ? Speed
Wk = m·V² / 2
V = √ (2·W/m)
V = √ (2·110250 / 180) = 35 m/s or V ≈ 126 km/h
you are trying to open a door that is stuck by pulling on the doorknob in a direction perpendicular to the door. if you instead tie a rope to the doorknob and then continue to pull in the same direction (i.e., perpendicular to the door) with the same force, how does the torque you exert on the door change?
The torque about the center of mass is the same as in a direction perpendicular to the door.
What is torque?The rotational equivalent of a force in physics and mechanics is called torque. Depending on the subject matter, it may also be referred to as the moment, moment of force, rotational force, or turning effect. torque symbolizes a force's ability to cause a change in the body's rotational motion around center of mass. The idea was developed as a result of Archimedes' studies on the application of levers. Similar to how a linear force pushes or pulls an object, torque is a twist about a particular axis. The ratio of the force's magnitude to the angle at which the force's line of action is perpendicular to the axis of rotation is known as the torque.
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The same Vegan "meatball" is thrown straight up into the air at a velocity of 21 m/s. It is allowed to fly upward and back down to the height it was originally thrown. What is the Vegan "meatball's" velocity at this moment.
When the Vegan "meatball's" velocity is at its highest position at this moment, its velocity is zero, 0m/s.
A projectile's velocity is zero at its highest point. A projectile's acceleration is zero at its maximum point. The vertical component of a projectile's velocity is suddenly zero (vy = 0 m/s) when it reaches its greatest height.
When vy = 0, the apex—the highest point in any trajectory—is reached. We apply the equation v2y=v20y2g(yy0) to calculate y because we know the initial position, initial velocity, and end velocity.
Since the projectile is moving uphill against the force of gravity, its velocity is beginning to slow down. When the vertical velocity eventually falls to zero, the bullet quickly accelerates downward due to gravity.
A projectile's horizontal velocity is constant (a never changing in value), and Gravity causes a downward vertical acceleration with a magnitude of 9.8 m/s/s. A projectile's vertical velocity fluctuates by 9.8 m/s per second, A projectile's vertical motion is unrelated to its horizontal motion.
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Who was awarded the highest-ever rank in the u. S. Armed forces? george patton douglas macarthur george washington dwight d. Eisenhower.
He attained the rank of military officer during the combat on the Western Front in World War I and was once more nominated for a Medal.
How do you define forces?The pushing or push on a phalanx item alters its speed. An unseen factor is an agent that possesses the power to change the resting or traveling position of a body. It has a direction as well as a quantity.
What kind of force is it?Contact forces and non-forces are two different kinds of forces. Nuclear force, gravitational force, frictional force, magnetic force, electrostatic force, spring force, and others are a few examples of forces.
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summarize the energy transformations that occur when a tennis racket hits a tennis ball.
Answer:
See explanation...
Explanation:
the kinetic energy of the moving tennis racket is converted (not transformed) to the kinetic energy of the tennis ball.
Since not much description is given here, I didn't include the potential energy of the tennis ball. But in normal cases, the kinetic energy of the tennis ball would be converted to potential energy of the ball, and it falls back down after some time (because of gravity) and slows down due to friction on earth- kinetic energy is converted to heat energy because of friction.
other types of energy are not stated since they can be negligible.
When is the total momentum of a system conserved? A. Always B. If the system is isolated C. If the forces are conservative D. Never; it's just an approximation.
The total momentum of the system is conserved if the system is isolated. option c.
Momentum :
It is the product of particles mass and velocity. It is a vector quantity.Its unit is Ns (Newton-second).formula of momentum is given as :
p= mv
where,
p = momentum of the body
m = mass of the body
v = velocity of the body
Total momentum offer system is equal to the vector sum of all the system's component masses.
A system that is an isolated system does not interact with its environment.
The total momentum of the system is conserved if the system is isolated. option c.
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What is concave lens?
Answer:
Diverging Lens.
Explanation:
Concave lenses have at least one surface curved inside. A concave lens is also known as a diverging lens because it is shaped round inwards at the centre and bulges outwards through the edges, making the light diverge. They are used to treat myopia as they make faraway objects look smaller than they are.
Two pure tones are sounded together and a particular beat frequency is heard. What happens to the beat frequency if the frequency of one of the tones is increased?.
Since it is unclear which of the two frequencies is being raised, the beat frequency will rise if the frequency of the higher-frequency note is raised. On the other hand, if the frequency of the lower frequency note is raised, the beat frequency decreases.
what is frequency?
A recurring event's frequency is measured by how many times it occurs in a unit of time. To emphasize distinctions with spatial and angular frequencies, respectively, it is also sometimes referred to as ordinary frequency or temporal frequency.
Frequency is an essential property for characterizing the temporal rate of change found in oscillatory and periodic phenomena, such as mechanical vibrations, audio signals (sound), radio waves, and light, in science and engineering.
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Since it is unclear which of the two frequencies is being raised, the beat frequency will rise if the frequency of the higher-frequency note is raised. On the other hand, if the frequency of the lower frequency note is raised, the beat frequency decreases.
What is frequency?
A recurring event's frequency is measured by how many times it occurs in a unit of time. To emphasize distinctions with spatial and angular frequencies, respectively, it is also sometimes referred to as ordinary frequency or temporal frequency.
Frequency is an essential property for characterizing the temporal rate of change found in oscillatory and periodic phenomena, such as mechanical vibrations, audio signals (sound), radio waves, and light, in science and engineering.
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determine the current magnitude and direction of flow in each of the three branches of the circuit below.
The current magnitude in each of the three branches of the circuit below are 1.25 A, 0.924 A and 0.31 A respectively
According to Ohm's law,
V = I R
V = Voltage
I = Current
R = Resistance
In loop 1,
33 I1 + 76 ( I1 - I2 ) - 48 + 20 ( I1 - I2 ) = 22
129 I1 - 96 I2 = 70 → ( 1 )
In loop 2,
76 ( I1 - I2 ) + 51 I1 + 8.5 + 42 I2 + 20 ( I1 - I2 ) = 0
- 96 I1 + 189 I2 = 56.5
I1 = ( 189 I2 - 56.5 ) / 96 → ( 2 )
Sub ( 2 ) in ( 1 ),
129 ( 189 I2 - 56.5 ) / 96 - 96 I2 = 70
( 24381 I2 - 7288.5 ) / 96 = 96 I2 + 70
24381 I2 - 7288.5 = 9216 I2 + 6720
15165 I2 = 14008.5
I2 = 0.924 A
I1 = ( 189 * 0.924 - 56.5 ) / 96
I1 = 1.25 A
I3 = I1 - I2
I3 = 1.25 - 0.924
I3 = 0.31 A
Therefore, the current magnitude in each of the three branches of the circuit below are:
I1 = 1.25 AI2 = 0.924 AI3 = 0.31 AThe given question is incomplete. The complete question is:
Determine the current magnitude and direction of flow in each of the three branches of the circuit below. The circuit is shown in the image attached.
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Complete combustion of 1.0 metric ton ofcoal (assuming purecarbon) to gaseous carbon dioxide release 3.3x10¹⁰ j of heat. Convert this energy to (a) kilojoules; (b) kilocalories
Complete combustion of 1.0 metric ton of coal (assuming pure carbon) to gaseous carbon dioxide release 3.3x10¹⁰ j of heat. a) energy converted into kilojoules will be 3.3 * [tex]10^{7}[/tex] kJ
b) energy converted into kilocalories will be 7.882 * [tex]10^{6}[/tex] kcal
Heat released = 3.3x10¹⁰ j
a) 1 J = [tex]10^{-3}[/tex] kJ
3.3x10¹⁰ j = 3.3x10¹⁰ * [tex]10^{-3}[/tex] = 3.3 * [tex]10^{7}[/tex] kJ
b) 1J = 0.23885 = 2.3885 * [tex]10^{-4}[/tex] kcal
3.3x10¹⁰ j = 3.3x10¹⁰ * 2.3885 * [tex]10^{-4}[/tex] = 7.882 * [tex]10^{6}[/tex] kcal
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The energy flux from the sun has a peak value of around 1500 W/m2, and solar cells are around
15% efficient. Estimate the area needed to satisfy US energy needs using solar cells, using the
estimates that there are about 350 million people in the US and that we use an average of 90
kW/person. Also assume that there are about 6 hours of "peak" sunlight per day. Answer in square
kilometers (do not put units in your answer, however).
Answer:
Power required = 3.5E8 * 9.0E4 = 3.2E13 (watts)
Power supplied = 1.5E3 * .15 * 3600 * 6 (watts / m^2) * A
= 1.5E3* .15 * 3600 * 6 = 4.9E6 * A
A = 3.2 / 4.9 * E7 = 3.2 / 4.9 * 10 = 6.5 km*2 (1 km^2 = 10E6 m^2)
Note: 1 W = 1 J / sec 1 kw = 1000 W
The area needed to satisfy US energy needs using solar cells 6.5 km²
What is energy?Energy is the ability or capability to do tasks, such as the ability to move an item (of a certain mass) by exerting force. Energy can exist in many different forms, including electrical, mechanical, chemical, thermal, or nuclear, and it can change its form.
Power required = 3.5E8 * 9.0E4 = 3.2E13 (watts)
Power supplied = 1.5E3 * .15 * 3600 * 6 (watts / m^2) * A
= 1.5E3* .15 * 3600 * 6 = 4.9E6 * A
A = 3.2 / 4.9 * E7 = 3.2 / 4.9 * 10
= 6.5 km*2
The area needed to satisfy US energy needs using solar cells 6.5 km².
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how fast will an electron be traveling after being ejected from the electron gun if the voltage is set to 500 v? for full credit: (1) show your work, (2) show explicitly how the units simplify, and (3) express your answer as a percentage of the speed of light. attach a separate sheet of paper if needed.
The speed of the electron ejected from the electron gun is 13.25 x 10^6 m/s
How do you define electrostatic force?
The attraction or repulsion between particles that electrostatic forces produce is due to their electric charges. In honour of French physicist Charles-Augustin de Coulomb, who first characterized the force in 1785, this force is also known as the Coulomb force or Coulomb interaction.Using Coulomb's law, one may determine the strength or force of the attraction or repulsion between two charged bodies:
F = kq1q2/r2
In this case, F is the force, k is the proportionality factor, q1 and q2 are two electric charges, and r is the separation between their centres.
Let us assum that the electron from the electron gun is ejected and accelerated in a vacuum.
Therefore if we neglect the gravitational force we see that the entire electrical potential energy is changed into kinetic energy.
According to the given informations:
Ki = initial kinetic energy of the electron = 0
Kf = final kinetic energy of the electron = mv^2/2
Ui = initial potential energy of the electron = qV
Uf = final potential energy of the electron = 0.
From the law of Conservation of energy we know,
Ki + Ui = Kf + Uf.
Putting the values we have,
0 + qV = mv^2/2 +0
qV = mv^2/2
Solving the above equation we find v,
v = √2qV/m
= √ 2 x
= √2 (−1.60×10^−19C) (−500J/C) / 9.11×1^−31kg−
= √175.6 x 10^12
= 13.25 x 10^6 m/s
Hence, the speed of the electron is 13.25 x 10^6 m/s
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the following images show five planets in our solar system. rank these planets from left to right based on their average surface (or cloud-top) temperature, from highest to lowest. (not to scale.)
Highest to Lowest temperature:
MercuryEarthMarsJupiterNeptuneWhat is average surface temperature?Planetary surface temperatures range from over 400°C on Mercury and Venus to below -200°C on distant planets. The factors that determine temperature are the complex balance of heat received and lost.
For these five planets, temperature correlates with distance from the Sun. The closer to the sun, the hotter the earth. Note, however, that this is not always the case, as the planet's temperature also depends on its reflectance and the strength of the greenhouse effect (if present). For example, although Venus is almost twice as far from the Sun, the average temperature on Venus is higher than on Mercury due to the greenhouse effect.
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A ball has a mass of 50g and is revolving at the end of a string in a circle with a radius of 40cm. The Ball moves with a speed of 2.5m/s, or one revolution per second. What is the horizontal component of the tension needed to produce this acceleration (in N)?
0.781 N is the horizontal component of the tension needed to produce this acceleration.
F=ma
T=ma
m= mass=0.05
a= centripetal acceleration =15.6
T=ma
T=0.05×15.6
T=0.781 N
When pressures on opposing ends are tugging on a rope, thread, wire, or something similar, tension is a contact force communicated through it. For instance, the rope attaching a tire swing to a limb of a tree is under strain. Gravity pulls the rope downward, while the upward pull is caused by a branch that is resisting the rope's tug tension, which is just a pulling force. A slack rope has no tension when one pushes on it. As a result, in a free-body diagram, the force of tension must always be shown in the direction that the string is pulling the item.
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situation where middle polarizer is rotated. suppose the middle polarizer is rotated at 100 revolutions per minute. how many times per minute will you observe the light change from bright (max intensity) to dark (min intensity)? this effect, although not normally done with mechanical rotation, is the basis for making optical modulators that are used in high-speed digital communication systems. can you please explain? thanks
When middle polarizer is rotated rotated at 100 revolutions per minute we can take following steps into consideration-
Weight the 20gm of sugar and dissolve the whole of it in 60cc of distilled water and filter the solution by keeping the filter paper in a funnel in clean beaker. We can add distilled water to make the volume of solution equal to 100 cc. This 20% solution i.e. 0.20gm/cc.Now take 50 cc of 20% solution in measuring cylinder and add 50cc distilled water to form 10% solution. Pour it in beaker labeled as 10% solution.Now take 50cc of 10% solution and add 50cc of distilled water in it to form 5% solution.This effect although not normally done with mechanical rotation, is the basis for making optical modulators that are used in high-speed digital communication systems by inserting the thermometer in solution and note down the temperature.
Remove the caps of polarimeter glass tube and measure the length of tube.
Setting up of sodium source in front of slit will be placed at the principal focus of lens of polarimeter.
[tex]Rotation=\alpha =\frac{\beta }{y}[/tex]
β is the mean angle of rotation and y means length of polarimeter tube in decimeter.
[tex]y=\frac{len. of polarimeter}{10}[/tex]
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HELP HELP!!!!!!!!!!!!!!!!
Magnetic force is used in: A door catch or a latch on kitchen cabinet
and A directional compass.
Electric force is used in: Two shocks stacks together coming out of a clothes dryers and An air filter that traps dust and ion particle.
What is magnetic force?Electromagnetic force is a result of charge motion, which also produces magnetic force. We know that a moving charge creates a magnetic field around itself. In this situation, the magnetic force can be thought of as a force that results from magnetic fields interacting.
A door catch or a latch on kitchen cabinet and a directional compass are example of use of magnetic field.
Two shocks stacks together coming out of a clothes dryers and an air filter that traps dust and ion particle are example of use of etectric force.
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A ball is dropped from rest from a height of 1.88 m. How long does it take to strike the ground? (use g = 10 m/s2)
A. 0.43 seconds
B. 0.38 seconds
C. 0.61 seconds
D. 0.19 seconds
It will take the ball 0.61 second of time to strike the ground. Option C is the right answer.
Motion Under GravityThe motion of an object under gravity is the object' s vertical motion under the influence of acceleration due to gravity.
Given that a ball is dropped from rest from a height of 1.88 m. Since the ball was dropped,
Initial velocity u = 0The height h = 1.88 mAcceleration due to gravity g = 10 m/s²Time t = ?How long it takes, that is, the time taken to strike the ground can be calculated by using the formula
h = ut + 1/2gt²
Substitute all the parameters into the formula
1.88 = 0 + 1/2 × 10 × t²
1.88 = 5t²
t² = 1.88/5
t² = 0.376
t = √0.376
t = 0.61 s
Therefore, the time taken for the ball to strike the ground is 0.61 s
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Which of the following is NOT a clue to the formation of the solar system?
A. Uranus has a large tilt to its rotation axis.
B. The number of small rocky planets is equal to the number of large gas-rich planets.
C. There are a large number of small rocky and icy objects in different regions of the solar system.
D. The planets and moons generally orbit in the same plane.
E. The Earth has an unusually large moon.
Option (B) is not a clue to the formation of the solar system i.e. the number of small Rocky planets is equal to the number of large gas rich planets.
Option (A) Uranus is the 7th planet in our solar system that is mostly known for being the planet that is "lying on its back".Uranus rotational axis tilts almost 98° and it looks like the planet is rotating on its side.
Option (B) The gas giants have atmosphere that are mostly hydrogen and helium, they do not have a well-defined surface and there is no clear boundary between where the atmosphere ends and the surface starts. Sometimes, the gas planets are so much larger than the rocky planets, the atmosphere grow faster than the solid part of the planet. So , we can't say that the number of small Rocky planets is equal to the number of gas rich planets.
Option (C) Asteroids are large no. of small rocky and icy object that orbits the sun. There are lots of asteroids in our solar system.
Option (D) All the planets, asteroids,meteoroids and comets in the solar system orbits in the same plane and this is called heliocentric orbit. During the solar system's formation, the planets formed out of a disk of dust which surrounded the sun, because that disk of dust was a disk, all in a plane, all of the planets formed in a plane as well and the planets and moons orbits in the same plane.
Option (E) Most moons are captured from bits of rocks left over from the formation of the planet but our moon is probably the result of a very big bit of rock hitting the early earth and splitting into two and this results in the formation of our natural satellite moon which is 3,84,000km away and that's why Earth has an unusually large moon.
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5. Cyclists are travelling around a track at 14m/s. When they leave it they
accelerate from 14m/s to 18m/s at a steady rate, which takes them 3 seconds.
What distance did they travel in this time?
The distance travel by the cyclists in the given time is 48 m.
Acceleration can be defined as the rate at which velocity changes with time, in terms of both speed and direction.
Acceleration is a vector quantity.
Initial velocity = 14 m/s
Final velocity = 18 m/s
Acceleration = final velocity- initial velocity / time taken
a = [tex]\frac{18 m/s - 14 m/s}{3 s}[/tex]
a = [tex]\frac{4}{3}[/tex] m/s^2
Now, for distance we can use distance formula
s = ut + 1/2 at^2
=14 × 3 + [tex]\frac{1}{2}[/tex] × [tex]\frac{4}{3}[/tex] × 3^2
=42 + 6
=48 m
Hence, the distance travel by the cyclists is 48 m.
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A certain liquid sample has a volume of 14. 7 ml and a mass of 22. 8 grams. Calculate the density.
The density of the liquid sample is 1.52 g/ml.
Density is the substance's mass consistent with the unit of quantity. The symbol most customarily used for density is ρ, despite the fact that the Latin letter D can also be used. Density is the size of ways tightly a cloth is packed together. it's far defined as the mass consistent with unit quantity.
ρ = m/V, wherein ρ is the density, m is the mass of the item and V is the quantity of the object.
Calculation:-
Density = mass/volume
= 22.8/14.7 g/ml
= 1.52 g/ml
The density is of two types, one is absolute density, and the alternative is relative density. Relative density is also called unique gravity, which is the ratio of the density of a material to the density of a reference material. typically, the reference fabric is water.
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if a ball is given a push so that it has an initial velocity of 4 m/s down a certain inclined plane, then the distance it has rolled after t seconds is given by the following equation.
Using the concepts of momentum, we got that 13m/sec is the velocity of the ball after 2 sec if the distance the ball has rolled after t seconds is given by s(t) = 5t + 2t2 equation.
Velocity is defined as the derivative of displacement with respect to time
v= ds/dt
The given equation of distance is
s(t) = 5t + 2t² : distance that the ball has rolled after t seconds
v= 4 m/s : initial velocity
t= 2 s
Problem development
s(t) = 5t + 2t²
Using differentiability
v= ds/dt= 5 + 4t : velocity of the ball in function of the time
We replace t =2 s in the equation of velocity
v= 5 + 4(2)
=>v=5+8
=>v=13m/sec.
Hence, if a ball is given a push so that it has an initial velocity of 4 m/s down a certain inclined plane, and the distance it has rolled after t seconds is given by the following equation s(t) = 5t + 2t2,then the velocity of the ball after 2 sec is 13m/sec.
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(Complete question) is:
If a ball is given a push so that it has an initial velocity of 4 m/s down a certain inclined plane, then the distance it has rolled after t seconds is given by the following equation. s(t) = 5t + 2t2 . Find the velocity after 2 seconds.
The American bullfrog (Rana catesbeiana) can jump a distance of
nearly 15 times its length! If a bullfrog starts on a horizontal log and
leaps with a velocity of 4.40 m/s at an angle of 37.0° to the horizontal,
what distance can it cover?
Answer:
Approximately [tex]1.90\; {\rm m}[/tex] (assuming that [tex]g = 9.81\; {\rm m\cdot s^{-2}}[/tex] and that air resistance on the bullfrog is negligible.)
Explanation:
It is given that the initial velocity [tex]u[/tex] is at an angle of [tex]\theta = 37.0^{\circ}}[/tex] above the horizontal. Therefore:
Initial vertical velocity: [tex]u_{y} = u\, \sin(\theta) \approx 2.64799\; {\rm m \cdot s^{-1}}[/tex].Initial horizontal velocity: [tex]u_{x} = u\, \cos(\theta) \approx 3.51400\; {\rm m \cdot s^{-1}}[/tex].
If air resistance on the bullfrog is negligible, final vertical velocity right before landing will be the opposite of the initial vertical velocity:
[tex]v_{y} = (-u_{y}) = (-2.64799)\; {\rm m\cdot s^{-1}}[/tex].
Change in vertical velocity:
[tex](v_{y} - u_{y}) = (-2.64799) \; {\rm m\cdot s^{-1}} - 2.64799 \; {\rm m\cdot s^{-1}} \approx (-5.29598)\; {\rm m\cdot s^{-1}}[/tex].
Vertical acceleration of the bullfrog will be [tex]a = (-g) = (-9.81)\; {\rm m\cdot s^{-2}}[/tex] while the frog is in the air. Therefore, time required for the velocity to change will be:
[tex]\begin{aligned} t &= \frac{v_{y} - u_{y}}{a_{y}} \\ &= \frac{v_{y} - u_{y}}{(-g)} \\ &\approx \frac{(-5.29598)\; {\rm m\cdot s^{-1}}}{(-9.81)\; {\rm m\cdot s^{-2}}} \\ &\approx 0.53985\; {\rm s}\end{aligned}[/tex].
If air resistance on the bullfrog is negligible, horizontal velocity will be constant: [tex]v_{x} = u_{x} \approx 3.51400\; {\rm m\cdot s^{-2}}[/tex]. After [tex]t \approx 0.53985\; {\rm s}[/tex] in the air, the horizontal displacement of the bullfrog will be:
[tex]\begin{aligned}x_{x} &= v_{x}\, t \\ &\approx 3.51400\; {\rm m\cdot s^{-1}} \times 0.53985\; {\rm s} \\ &\approx 1.90\; {\rm m} \end{aligned}[/tex].
Therefore, this bullfrog will cover a distance of approximately [tex]1.90\; {\rm m}[/tex].