The kinetic energy of the blocks that is lost due to the collision is 8.64 J.
What is the initial speed of the smaller block?The initial speed of the smaller block is calculated by applying the following equation.
m₁u₁ + m₂u₂ = v(m₁ + m₂)
where;
m is the mass of the blocksu is the initial velocity of the blocksv is the common velocity of the blocks after the collision9u₁ + 27(0.5) = 0.9(9 + 27)
9u₁ + 13.5 = 32.4
9u₁ = 18.9
u₁ = 18.9/9
u₁ = 2.1 m/s
The total initial kinetic energy of the blocks is calculated as follows;
K.Ei = ¹/₂m₁u₁² + ¹/₂m₂u₂²
K.Ei = ¹/₂(9)(2.1)² + ¹/₂(27)(0.5)²
K.Ei = 23.22 J
The final kinetic energy of the blocks is calculated as follows;
K.Ef = ¹/₂(m₁ + m₂)v²
K.Ef = ¹/₂(9 + 27) x (0.9)²
K.Ef = 14.58 J
The change in the kinetic energy of the block is calculated as;
ΔK.E = K.Ef - K.Ei
ΔK.E = 14.58 J - 23.22 J
ΔK.E = -8.64 J
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Consider the Atwood Machine, assuming a massless pulley. Assume m1 > m2. Using N2, we found the acceleration of the system is: a = g(m1 − m2)/(m1 + m2) and the tension was equal. Now take into account the mass of the pulley:
a) Suppose m1 = 0.7 kg and m2 = 0.4 kg. What would the system acceleration be for the pulley?
b) What is the net torque acting on the pulley in terms of the tensions T1, T2, and the pulley radius R? What is the net force acting on each mass in terms of T and weight?
c) Use Newton's 2nd, Rotational N2, and assume the string doesn’t “slip” (at = αR) to find the acceleration of the system if the mass of the pulley is 5 kg.
The system acceleration for the pulley having masses m1 = 0.7 kg and m2 = 0.4 kg Is 35.93 [tex]m/s^2[/tex].
What is Newton's Second Law?Newton's second law provides a detailed explanation of how a force can alter a body's motion. It is believed that a body's momentum varies over time at a rate equal to the force acting on it in both direction and amplitude. The combined effects of a body's mass and velocity determine its momentum.
Given:
The mass, m₁ = 0.7 kg,
m₂ = 0.4 kg,
Calculate the system acceleration by the following formula,
a = g(m1 − m2)/(m1 + m2)
Here a is the acceleration.
Substitute the values,
a = 9.8 * (0.7 - 0.4 ) / (0.7 + 0.4)
a = 35.93 [tex]m/s^2[/tex]
Therefore, the system acceleration for the pulley is 35.93 [tex]m/s^2[/tex].
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The rock to the right is sitting at the top of a ramp.
I wonder how much work it required to get that rock up
there.
[ ]
Can you figure it out? (This is not a yes or no question:
solve!)
The amount of work required to move the rock of mass 95 kg up a ramp of 100 m is 93100 J.
What is work?Work can be fined as the product of force and distance.
To calculate the amount of work required to get the rock up, we use the formula below.
Formula:
W = mgh........... Equation 1Where:
W = Amount of workm = Mass of the rockg = Acceleration due to gravityh = Height of the rampFrom the question,
Given:
m = 95 kgh = 100 mg = 9.8 m/s²Substitute these values into equation 1
W = 95×100×9.8W = 93100 JHence, the amount of work required is 93100 J.
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Which kind of wave is a wave on the electromagnetic spectrum?
O mechanical wave
O longitudinal wave
O transverse wave
O matter wave
Mechanical wave is a kind of wave is a wave on the electromagnetic spectrum.
What is electromagnetic spectrum?Electromagnetic (EM) waves are cross waves. Their vibrations or oscillations are swapped in electrical and magnetic fields at right angles to the direction of wave travel. The radiation is explained by the amount of energy found in the photons. Radio waves have photons with low energies, and microwave photons ..Electromagnetic waves with smaller wavelengths and higher frequencies include ultraviolet light, X-rays, and gamma rays. Electromagnetic waves with longer kinds of Electromagnetic Waves. Radio Waves have the longest wavelengths of all electromagnetic waves.
So we can conclude that the different types of waves are mechanical and electromagnetic waves. Mechanical waves are divided into transverse and longitudinal waves.
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A cube of wood with a density of 0.780 g/cm' is 10.0 cm on each side. When the cube is placed in water, what buoyant force acts on the wood? (pw 1.00 g/cm')
The buoyant force acts on the cube of wood with a density of 0.780 g/[tex]cm^3[/tex] And 10.0 cm on each side is 7.644 Newton.
What is density?The density is the mass of a material substance per unit volume. d = M/V, where d is density, M is mass, and V is volume, is the formula for density. Grams per cubic centimeter are a typical unit of measurement for density.
As an illustration, the density of Earth is 5.51 grams per cubic centimeter, whereas the density of water is 1 gram per cubic centimeter.
Given:
The density of wood, ρ = 0.780 g/[tex]cm^3[/tex],
The Side of wood, a = 10 cm,
Calculate the buoyant force by the following formula,
F = - ρ * g * V,
Here, F is the buoyant force.
Substitute the values,
F = - 0.780 * 9.8 * [tex]10^3[/tex] * [tex]10^{-3}[/tex]
F = 7.644 Newton
Therefore, the buoyant force acts on the cube of wood with a density of 0.780 g/[tex]cm^3[/tex] is 10.0 cm on each side is 7.644 Newton.
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I know this isn’t the right subject but i need help
Expository with an a anecdote and explain how specific life even impact the character of an individual
The current state of research offers some evidence that life events can cause changes in personality traits and that various life events may connect differently to various trait domains.
What is anecdote?
A brief narrative or account abou life events changet a person or event that is typically humorous, instructive, entertaining, or biographical in nature is known as an anecdote.
How do life events change your personality?
These ideas contend that because life events alter, interrupt, or reroute people's habits of thought, feeling, and action, they have long-lasting consequences on personality traits.
Hence is a changes in personality traits a correct answer.
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what is the angle between a = 3.0i - 4.0j and b=2.0i +3.0k?
The answer is 70.6°
Very Important, I need the answer
Answer:
A
Explanation:
A constant velocity means the position graph has a constant slope. It's a straight line sloping up.
How long does it take a 100 g sample of As-81 to decay to 6.25 g? (half-life of As-81 is 33 seconds)
Answer:
Explanation:
m₀ = 100 g
m = 6.25 g
T = 33 s
_____________
t - ?
Radioactive decay constant:
λ = ln 2 / T = 0.693 / 33 ≈ 0.021 s⁻¹
Law of radioactive decay:
[tex]m=m_{0} e^{-\lambda t} \\[/tex]
[tex]e^{-\lambda t} = \frac{m}{m_0} \\[/tex]
[tex]ln (e^{-\lambda t}) = ln(\frac{m}{m_0} ) \\[/tex]
[tex]-\lambda t = ln (\frac{m}{m_0})[/tex]
[tex]t = -\frac{ln(\frac{m}{m_0}) }{\lambda}[/tex]
t = - ln (6.25/100) / 0.021 ≈ 132 s
What kind of organisms do binary fission?
Answer:
Prokaryotes such as E. coli, Archaea as well as eukaryotes such as euglena reproduce through binary fission.
Explanation:
Answer:
Prokaryotes such as E. coli, Archaea as well as eukaryotes such as euglena reproduce through binary fission.
Explanation:
.Given the displacement vectors A = 6f-4j+8k B = 2î+4ƒ^ − 14k
Find the magnitude and the unit vector of the vector 0.5A + 0.5B
Answer:
Explanation:
A = 6i - 4j + 8k
B = 2i + 4j - 14k
A + B = (6+2)i + (-4+4)j + (8-14)k
A + B = 8i +0j -6k
A + B = 8i - 6k
(1/2)(A + B) = 4i - 3k
d = √ (4² + 3²) = 5
e = (4/5)i -(3/4)j
Please choose one of the following topics and write a short summary of the concept (50-100 words). Please ask a question about the chosen topic.
Topic Chosen: DARK MATTER / DARK ENERGY
The short summary of the concept of dark matter and dark energy is given here.
What is dark matter?An estimated 85% of the universe's mass is assumed to be made up of dark matter, a hypothetical type of stuff. Because it does not appear to interact with the electromagnetic field—that is, it does not absorb, reflect, or emit electromagnetic radiation—dark matter is referred to as being "dark," making it challenging to detect.
Numerous astrophysical observations support the existence of dark matter, including gravitational effects that cannot be described by the gravity theories currently in use without the presence of more matter than can be observed. Because of this, the majority of scientists believe that dark matter is prevalent in the universe and has significantly influenced both its structure and evolution.
What is dark energy?Dark energy is an undiscovered type of energy that has the largest effects on the cosmos according to physical cosmology and astronomy. Supernova observations provided the first direct proof for its existence by demonstrating that the cosmos is expanding faster than ever rather than at a fixed rate. It is necessary to understand the universe's origins and initial elements in order to comprehend its evolution.
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A rubber band (in the form of a loop) is to be launched horizontally from a height of 1.0m. During the first launch, the rubber band is stretched 2.0 cm and the rubber band lands at a horizontal distance of 3.5 m from the point of launch. For the second launch the rubber band is stretched 4.0 cm. How far does it travel horizontally this time? If the same rubber band were to be stretched 4.0 cm, but aimed vertically, how high does it go?
The rubber band travels horizontally 7.0 cm in second time.
Given parameters:
the rubber band is stretched = 2.0 cm.
And, the rubber band travels = 3.5 cm.
Secondly, the rubber band is stretched = 4.0 cm.
As force is directly proportional with stretching and landing at a horizontal distance, it travels horizontally in second time
= 4.0 cm x 3.5 cm/ 2.0 cm.
= 7.0 cm.
The vertical movement can't be measured as a new gravitational force comes in play in this case.
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Which side of a cuboid should be placed on the ground to exert maximum pressure?
a) The smallest side
b) The largest side
c) The longest side
d) Each side will exert the same pressure on the ground
A sprinter with a mass of 68 kg reaches a speed of 8 m/s during a race. Find the sprinter's linear momentum (in kg · m/s). (Enter the magnitude.)
The momentum of the sprinter of mass and velocity of 68 kg and 8 m/s respectively is 544 kgm/s
What is momentum?Momentum can be defined as the product of mass and velocity of a body.
To calculate the linear momentum of the sprinter, we use the formula below.
Formula:
M = mv........... Equation 1Where:
M = Linear momentum of the sprinterm = Mass of the sprinterv = Velocity of the sprinterFrom the question,
Given:
m = 68 kgv = 8 m/sSubstitite the values into equation 1
M = 68×8M = 544 kgm/sHence, the momentum of the sprinter is 544 kgm/s.
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The linear momentum of the sprinter with a mass of 68 kg that reaches a speed of 8 m/s during a race is 544kgm/s.
How to calculate momentum?The momentum of a body in motion is the tendency of a body to maintain its inertial motion. It is the product of its mass and velocity, or the vector sum of the products of its masses and velocities.
The linear momentum of a body can be calculated as follows:
p = m × v
According to this question, a sprinter has a mass of 68kg and reaches a speed of 8 m/s during a race. The momentum can be calculated as follows:
p = 68kg × 8m/s
p = 544kgm/s
Therefore, 544kgm/s is the linear momentum of the sprinter.
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A car rounding a corner has an acceleration
of 5m/s². If it rounds a corner with twice the
radius at the same speed, what would be its new
acceleration?
5/4 m/s^{2} would be its new acceleration .
What is centrifugal acceleration ?
The simplest case of circular motion is uniform circular motion, where an object moves in a circular trajectory with constant velocity. Note that the linear velocity of an object in circular motion is constantly changing because, unlike velocity, it is constantly changing direction. From kinematics we know that acceleration is a change in velocity, either in magnitude or direction, or both. Therefore, an object in uniform circular motion will always be accelerated even if the magnitude of its velocity is constant. You can feel this acceleration every time you get in the car while cornering. Keeping the handle steady while turning and moving at a constant speed creates a smooth circular motion. What you will notice is a feeling of skidding (or skidding depending on speed) out of the center of the turn.
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The absolute Temprature of an ideal diatomic gas is quadrupied. What happens to the average sp eed of molecules?
If the absolute temperature of an ideal diatomic gas is quadrupled, then, the average speed of molecules is doubled.
[tex][V_avg=\sqrt(8k *4T)/\pi m],[V_avg=2\sqrt(8kT) \pi m],[V_avg=2v_avg][/tex]
Speed (often abbreviated as "s") is a scalar variable that describes how much an object's location changes over time or how much it changes per unit of time. The average speed of an item in a period of time is the distance traveled by the object divided by the duration of the period.
Time divided by distance are the speed-related metrics.. The meter per second (m/s) is the SI unit of speed, while the kilometer per hour (kph) is the most often used unit of speed in daily life.
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An object of mass 3.0 kg starts from rest and moves along the x-axis. A net horizontal force is applied to the object in the +x direction. The Force-time graph is shown below. What is the net impulse delivered by the applied force?
Answer:
120
Explanation:
because it is horizontal
An object of mass 3.0 kg starts from rest and moves along the x-axis. A net horizontal force is applied to the object in the +x direction. The Force-time graph is shown below. The net impulse delivered by the applied force is 102 joule.
What is force ?A force is an influence that has the power to alter an object's motion. An object with mass can change its velocity, or accelerate, as a result of a force. An obvious way to describe force is as a push or a pull. A force is a vector quantity since it has both magnitude and direction.
Force is used to describe a body's tendency to modify or change its state as a result of an external cause. When force is applied, the body can also alter its size, shape, and direction. kicking a ball, pushing and pulling on the door, or kneading dough are a few examples.
We know the Impulse = Area of the Graph
= ( 6 × 4) + 0.5 × 2 × 6
= 30 sec
For First 4 sec
Acceleration = 6 ÷ 3
= 2 m/sec²
S = 0.5 × 2 × 4²
= 16 m
Therefore, work Done = 6 × 16
= 96 J
Then, Average force
= ( 6 - 0 ) ÷ 2
= 3 N
Acceleration = 1 m/sec²
S = 0.5 × 1 × 2²
= 2 m
Work = 3 × 2
= 6 J
Total Work = 96 + 6
= 102 J
Thus, The net impulse delivered by the applied force is 102 joule.
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Superman must stop a 120−km/h train in 150 m to keep it from hitting a stalled car on the tracks. If the train’s mass is 3.6×105 kg, how much force must he exert? Compare to the weight of the train (give as %). How much force does the train exert on Superman?
The force that Superman must exert is -1.33 * 10⁶ N
The force that must be exerted by Superman is 37.6 % of the weight of the train.
The force the train exerts on superman is 1.33 * 10⁶ N
What is the average acceleration of the train?The average acceleration of the train is determined from the equation of motion as follows:
v² = u² + 2as
where
v is final velocity = 0 m/s
u is initial velocity = 120 km/h
To convert km/h to m/s, we multiply km/h by 1000/3600
u = 120 * 1000/3600
u = 33.3 m/s
a = ?
s = 150 m
a = v² - u² / 2s
a = 0 - 33.3² / 2 * 150
a = 3.696 m/s²
Force that must be exerted will be:
Force = mass * accelerationForce = 3.6 × 10⁵ * 3.696 m/s²
Force = -1.33 * 10⁶ N
b. Weight of train = 3.6 × 10⁵ * 9.81
Weight of train = 3.53 * 10⁶ N
The ratio of the force and the weight of the train = (-1.33 * 10⁶ / 3.53 * 10⁶) * 100%
The ratio of the force and the weight of the train = 37.6%
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A sports car accelerates from rest to 103 km/h in 6.5 s. What is its average acceleration in m/s2?
The acceleration of the car is 57.04 [tex]m/s^{2}[/tex]
It is given that a sports car accelerates from rest to 103 km/h in 6.5 s.
So, Initial velocity (u) = 0 m/s { since the car starts from rest }
Final velocity (v) = 103 km/hr = 103 * 18/5 m/s = 370.8 m/s
Now, the time taken (t) = 6.5 seconds.
Acceleration is the measure of how fast the object's velocity changes with respect to time.
Now, Acceleration (a) = Change in velocity/Time taken
So,
[tex]a = \frac{v -u}{t}[/tex]
Putting all the values, we get
[tex]a = \frac{370.8 - 0}{6.5} =\frac{370.8}{6.5} = 57.04[/tex]
Hence, the acceleration of the car is 57.04 [tex]m/s^{2}[/tex]
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A 76 kg bike racer climbs a 1500-m-long section of road that has a slope of 4.3 ∘ . you may want to review ( pages 296 - 298) . part a by how much does his gravitational potential energy change during this climb
The gravitational potential energy change during this climb is 83,790 J.
What is the change in the gravitational potential energy?
The change in the gravitational potential energy of the bike racer is calculated as follows;
ΔP.E = mgh
where;
m is the mass of the bike racerh is the vertical height travelledg is acceleration due to gravityThe vertical height of the road is calculated as follows;
h = L sinθ
where;
θ is the slope of the roadL is the length of the roadh = 1500 x sin(4.3)
h = 112.5 m
ΔP.E = 76 x 9.8 x 112.5
ΔP.E = 83,790 J
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Which characteristic of Earth’s orbit are in agreement with Kepler’s second law
The features of Earth's orbit that concur with and conform to the pattern of Kepler's second law include the fact that Earth feels the largest gravitational pull when it is closest to the Sun.
In which of the following is Kepler's second law stated?According to Kepler's second rule, a planet moves in its ellipse so that a line drawn between it and the Sun and focused on it covers the same amount of space in the same amount of time.
What features distinguish the earth's orbit?The eccentricity of the Earth's orbit around the Sun, which is an ellipse, determines how far from a circle the orbit is (e). The perihelion, or point on the orbit that is closest to the Sun, and the apogee, or point most aphelion of the Sun.
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Whitch is true of high resistsncce wires
The longer a wire is, the higher the resistance will be.
Neither length (L) nor cross-sectional area (A) influences Rh. It totally depends on the type of material used to make the wire. It is somewhat dependent on temperature variation, but this variation is negligible and is disregarded for most purposes.
Let Resistivity be Rh and Resistance be R.
L for the wire's length and A for its cross-section.
This formula relates to resistance.
R=Rh*L/A
Rh, L, and A are the three parameters that determine resistance.
The resistance increases as the wire lengthen.
Less resistance is there the larger the cross-sectional area. (Put A in the denominator; the numerator is L.)
Only take into account the Length variable. As was previously said, shorter wires have lower resistance and vice versa.
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Shawn and his bike have a total mass of 49.9 kg. Shawn rides his bike 0.92 km in 15.4 min at a constant velocity. The acceleration of gravity is 9.8 m/s 2 . What is Shawn’s kinetic energy? Answer in units of J.
Answer:
0 J
Explanation:
KE = .5(m)(v2-v1)
if velocity is constant v2 = v1, then v2 - v1 = 0
therefore if (v2-v1) = 0, then KE must also be equal to 0
An adventurous ant finds herself at the end of a fan blade when it is switched on. It is a high speed fan with blades measuring 0.30 m long. If she has a mass of 0.22 g and can hold on to the fan blade with a maximum force of 0.0137 N, what is the maximum number of revolutions per minute the fan can run at before she will be flung off?
The maximum number of revolutions per minute the fan can run at before she will be flung off is 1,982.24 rev/min.
What is the maximum angular speed of the fan?
The maximum angular speed of the fan is calculated by applying the following kinematic equation.
From Newton's second law of motion,
F = ma
F = mv/t
F = m(ωr/t)
where;
m is the mass ω is the angular speed in rad/sr is the radius of the bladet is the time of the bladeω/t = F/mr
ω/t = (0.0137 N) / (0.00022 kg x 0.3 m)
ω/t = 207.58 rad/s
ω/t = (207.58 rad/s) x (1 rev / 2π rad) x (60 s / min)
ω/t = 1,982.24 rev/min
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On a sunny day with clear roads, Freddie is going 5 m/s over the speed limit with a deceleration of 2g and he runs a red light. What is his speed as he goes through the light?
Answer: The most widely accepted method of determining the posted speed limit is to set the speed limit at what is called the “85th percentile speed”, which is the speed at or below which 85 percent of the traffic is moving.
Explanation:
a mass of 2kg is supported by two cords which makes angle 30 degree and 50 degree with the vertical. calculate the tension in the two cords
So, this is the diagram of the described situation, the strings are attached to a rigid support at their one end and the other end is connected to the particle.
Let, the string making an angle of 45 with the horizontal has a tension of T 1 and
the one making an angle of 30 has a tension of T2.
Now,
what we have done is that we have taken the vertical and
horizontal components of the tension in the two strings.
Now,considering the system to be in equilibrium,
see the diagram,the vertical component of the strings i.e
(T 1 sin 45 & T 2 sin 30) together will act to balance the weight of
the particle(mg)
So,we can say, T 1 sin 45 + T 2 sin 30 = mg. ...(1)
From horizontal equilibrium,we can say, T 1 cos 45 must balance T 2 cos 30 ,
as no other force is present in horizontal direction.
So,T 1 cos 45 = T 2 cos 30. ...(2)
Given,
mg = 10 ⋅ 10 = 100N
So, solving equation 1 & 2 we get,
T 1 = 89.65N and, T 2 = 73.20N
A force F~ = Fx ˆı + Fy ˆ acts on a particle that
undergoes a displacement of ~s = sx ˆı + sy ˆ
where Fx = 3 N, Fy = −2 N, sx = 5 m, and
sy = 2 m.
Find the work done by the force on the
particle.
Answer in units of J.
Find the angle between F~ and ~s.
Answer in units of ◦
Answer:
Explanation:
Given:
F = Fₓ·i + Fy·j
S = Sₓ·i + Sy·j
Fₓ = 3 N
Fy = - 2 N
Sₓ = 5 m
Sy = 2 m
_________
A - ? - Work
α - ? - Angle
F = 3·i - 2·j
S = 5·i + 2·j
The work is numerically equal to the scalar product of the displacement force
A = (F·S) = 3·5 + (-2)·2 = 15 - 4 = 11 J
Modules:
| F | = √ (3² + (-2)² ) = √ (9 + 4) = √ 13
| S | = √ (5² + 2² ) = √ (25 + 4) = √ 29
Angle:
cos α = (F·S) / ( |F| · |S| ) = 11 / ( √13 · √29) ≈ 0,5665
α ≈ 55.5°
What is the best definition of a
wave
A. A wave is a disturbance that transfers matter.
B. A wave is electric charges that flow through
wires really fast.
C. A wave is a disturbance that transfers energy.
Answer: C
Explanation:
You are walking toward the back of a bus that is moving forward with a constant velocity. describe your motion relative to the bus and a point on the ground
You are travelling towards the back of the bus. If your walking speed is slower than the speed of the moving bus (which it generally is), your motion relative to a point on the ground will be travelling in the same direction as the moving bus, but at a slower rate.
What is speed?
Speed can be defined as the distance travelled by an object in relation to the time it takes to travel that distance. In other words, it measures how rapidly an object moves but does not provide direction. When we get direction with speed, we term it "velocity."
The SI unit system is most typically used to express speed. Speed is measured in metres per second, or m/s, because distance is measured in metres and time is recorded in seconds.
Speed is measured in metres per second (ms-1) and is symbolised by the letter "s."
The distance travelled is denoted by d and measured in meters (m).
The distance travelled per unit of time is referred to as speed. It is the rate at which an object moves. The magnitude of the velocity vector is represented by the scalar quantity speed. It lacks a sense of direction. A higher speed indicates that an object is travelling faster. Lower speed indicates that it is travelling more slowly. It has zero speed if it is not moving at all.
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what happens to the weight and mass of an object transported from earth to the moon
When an object transported from earth to the moon, its mass remains same but weight becomes 1/6th that on earth..
What is mass?In physics, mass is a quantitative measurement of inertia, a basic characteristic of all matter.
It essentially refers to a body of matter's resistance to changing its speed or location in response to the application of a force. The change caused by an applied force is smaller the more mass a body has.
What is weight?The amount of a body's weight indicates how much gravity is pulling on it. Weight is calculated using the method w = mg. Since weight is a force, it has the same SI unit as a force, which is the Newton (N).
So, mass of an object is intrinsic property of the object - it remains same in earth and in moon. But weight is the amount of gravitational attraction force. Moon has nearly 1/6th gravitational attraction field. So, the weight of the object on moon will be 1/6th that on earth.
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