When the spring undergoes simple harmonic motion and its mass is at maximum displacement then its instantaneous velocity is zero.
Simple Harmonic Motion:
Simple harmonic motion is a periodic motion in which the acceleration of the object undergoing the simple harmonic motion is directly proportional to the distance of the object from its equilibrium position and is always directed toward the mean position.
At the maximum displacement, the spring is under its greatest tension, which forces the mass upward. At the maximum displacement, the spring reaches its greatest compression, which forces the mass back downward again.
Therefore we get that when mass is at its maximum displacement from equilibrium its instantaneous velocity is zero.
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two ice skater, one is 60kg, the other 40kg. when the 60kg man pushes the 40kg woman with 120 n force, what will be the acceleation for the 40kg and 60 kg person respectively?.please enter only the number, no unit!
The acceleration for the 40kg and 60 kg person will be 3 m / s² and - 2 m / s² respectively if the 60kg man pushes the 40kg woman with 120 N force.
F = m a
F = Force
m = Mass
a = Acceleration
For 40 kg woman,
m = 40 kg
F = 120 N
a = F / m
a = 120 / 40
a = 3 m / s²
For 60 kg man,
According to Newton's third law of motion, for every action there will be an equal and opposite reaction. So the 40 kg woman will push back with a force of - 120 N.
a = - 120 / 60
a = - 2 m / s²
The negative sign indicates negative direction.
Therefore, the acceleration for the 40kg and 60 kg person will be 3 m / s² and - 2 m / s² respectively
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a 873-kg (1930-lb) dragster, starting from rest, attains a speed of 26.3 m/s (58.9 mph) in 0.59 s. find the average acceleration of the dragster during this time interval. what is the magnitude of the anverage net force on the dragster durng this time?
The average acceleration of the dragster during this time interval is 44.57 m/s² and the average net force on the dragster during this time is 38915N.
The initial speed U of the dragster is zero while the final speed V of the dragster is 26.3m/s. The director runs for a total of time t of 0.59 seconds.
According to the equation of motion,
V = U+at
Putting values,
26.3 = 0.59a
a = 44.57 m/s².
So, the acceleration of the dragster is 44.57 m/s².
The force on the director is given by,
F = ma
m mass of the dragster and a is the acceleration of the dragster.
F = 873×44.57
F = 38915N.
So, the net average force on the dragster during this time is 38915 Newton.
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What is the process that causes harmful materials to seep into the ground and move through rock and soil and contaminate ground water?.
which of the glass lenses above, when placed in air, will cause rays of light (parallel to the central axis) to converge?
Convex lenses when placed in the air, will cause rays of light (parallel to the central axis) to converge.
Converging lenses, commonly referred to as convex lenses, have thicker centers and narrower upper and lower margins. The edges are outwardly curled. This lens has the ability to concentrate a beam of parallel light rays coming from the outside onto a spot on the opposite side of the lens.
The image created is referred to be a genuine image when it is inverted relative to the object. On a screen, this kind of image can be recorded. When the object is positioned at a point farther than one focal length from the lens, a converging lens creates a true image.
A virtual image is one that cannot be produced on a screen and is formed when the image is upright in relation to the object. When an item is positioned within one focal length of a converging lens, a virtual image is created. It creates an enlarged image of the object on the same side of the lens as the image. It serves as a magnifier.
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A diver runs horizontally off the end of a 3.0-m-high diving board with an initial speed of 1.8 m/s. Find her y positions at the times t = 0.25 s , t = 0.50 s , and t = 0.75 s .
(a) At time, t = 0.25 s, the y position of the driver is 0.31 m.
(b) At time, t = 0.50 s, the y position of the driver is 1.2 m
(c) At time, t = 0.75 s, the y position of the driver is 2.76 m
What is the position of the driver?The position of the driver at the various time is determined by applying the following kinematic equation.
y = vt + ¹/₂gt²
where;
v is the initial vertical velocity of the drivert is the time of motion of the drivery is the vertical position of the driver at various timet is the time of motionSince the driver runs horizontally, the initial vertical velocity = 0
y = 0 + ¹/₂gt²
y = ¹/₂gt²
at time, t = 0.25 s, the y position of the driver is calculated as;
y = ¹/₂gt²
y = ¹/₂(9.8)(0.25)²
y = 0.31 m
at time, t = 0.5 s, the y position of the driver is calculated as;
y = ¹/₂gt²
y = ¹/₂(9.8)(0.5)²
y = 1.2 m
at time, t = 0.75 s, the y position of the driver is calculated as;
y = ¹/₂gt²
y = ¹/₂(9.8)(0.75)²
y = 2.76 m
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suppose that a microscope has an objective whose focal length is 1.00 mm and an eyepiece whose focal length is 25.0 mm. what is the magnifying power (m)) of the microscope? group of answer choices 25x 0.04x we need more information to calculate mp. 625x 160x
The ratio of the image's distance from the lens to the object's distance determines a lens's magnifying capability. Thus, the microscope's magnification factor m=m1m2.
Explain about magnifying power?Magnifying power is a lens's capacity to enlarge an image by how much. The least distance of distinct vision, or LDDV, and the focal length of the lens are directly correlated. Your eyes can easily focus on an object up to their LDDV.
By dividing the focal length of the scanning object (lens) by the focal length of the eyepiece, the magnifying power is computed. A 1x magnification power results in a 100% increase in the size of the thing being enlarged. A 1-inch object, for instance, would appear to be 2 inches at 1x.
The ratio of the angle the image at the eye occupies to the angle the object occupies is known as the magnifying power of the microscope.
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Select all that apply.
Salt dissolved in water is a solution, therefore _____.
A. salt and water are chemically combined
B. salt is not chemically bonded to water
C. salt and water retain their own chemical properties
D. the ratio of salt to water may vary
E. the quantity of salt and water is fixed
Answer:B
Explanation:explanation
a proton, traveling with a velocity of 4.1 106 m/s due east, experiences a magnetic force that has a maximum magnitude of 8.8 10-14 n and a direction of due south. what are the magnitude and direction of the magnetic field causing the force?
A particle travelling at a specific speed through a magnetic field experiences a force known as the magnetic force.
Magnetic Force:
A particle travelling at a specific speed through a magnetic field experiences a force known as the magnetic force. This relates to the cross-product of the magnetic field and velocity.
Answer and Explanation:
(a) The magnetic force is given by
F=qvBsinθ
q=1.60×10−19C , the charge of a proton
v is the velocity
B is the magnetic field
θ is the angle between the velocity and the magnetic field. Since the magnetic force is at maximum, then the velocity and the magnetic field is perpendicular.
Solving for the magnetic field:
B=F/qvsinθ= 9.0×10−14N/ (1.6×10−19 C)(3.7×106 m/s)sin90∘=0.15 T
By the right-hand rule, the direction of the magnetic field is upward, perpendicular to the earth's surface.
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A particle travelling at a specific speed through a magnetic field experiences a force understood as the magnetic force.
What is Magnetic Force?The magnetic force is a force that is felt by a particle moving in a magnetic field at a particular speed. This has to do with the magnetic field and velocity's cross-product.
(a) The magnetic force is given by
F=qvBsinθ
q=1.60×10−19C , the charge of a proton
v is the velocity
B is the magnetic field
The angle between the magnetic field and the velocity is called. The magnetic field and velocity are perpendicular because the magnetic force is at its greatest.
B=F/qvsinθ= 9.0×10−14N/ (1.6×10−19 C)(3.7×106 m/s)sin90∘=0.15 T
By the right-hand rule, the direction of the magnetic field is upward, perpendicular to the earth's surface.
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in which zone does the sun rotate more or less as a solid body, with all latitudes taking a similar amount of time to circle the sun's axis?
The radiative zone and core of the Sun are thought by scientists to revolve more like solid bodies than liquid ones. From the convective zone outward, the Sun's outer regions rotate at various rates that change with latitude.
What is latitudes?It is calculated using 180 fictitious lines that are drawn in circles east-west of the equator. Parallels are the names for these lines.Because the Sun is made of gaseous plasma, its rotation varies with latitude. At the equator, the rate of rotation is seen to be the quickest, and it slows down as latitude rises.Since it is made of gas and plasma, the rotational velocities of the gasses and plasma vary depending on where they are on the sun. Every 25 days, the gas and plasma close to the equator of the sun rotate around its axis.Polaris will appear lower in the sky as you move further south, and the sun will set at nighttime farther and more quickly.To learn more about latitudes refer to:
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a skier traveling 11.0 m/s reaches the foot of a steady upward incline and glides 15 m up along this slope before coming to rest. what was the average coefficient of friction?
The average coefficient of friction of the track on which the skier is travelling is 0.59.
According to work energy theorem, the work done by conservative forces and the non conservative forces on the body is equal to the change in kinetic energy of the body.
So here, we know that the skier is travelling with a speed of 11m/s and he glide a distance of 15 m.
Here, we can write,
Mgd + uMgd = ∆K
Where M is the mass of the body,
g ji is the acceleration due to gravity,
d is the distance travel by the glider,
K is the change in kinetic energy,
U is the coefficient of friction.
Putting values,
Mgd + uMgd = 1/2Mv²
2(gd + ugd) = v²
u = (v²/2-gh)/gd
u = ((11)²/2 -10×15)/10×15
u = 0.59
So, the average coefficient of friction is 0.59.
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a toy train is traveling along a circular track at a constant speed. the acceleration of the train is found to be 8.0 m/s2 . if the radius of the track is 0.5 m, what is the speed of the train?
The speed of the toy train travelling on a circle-shaped track is 2.0 m/sec also called velocity of the train.
How to find Speed ?Speed is calculated as follows: speed = distance * time. Knowing the units for distance and time is necessary to calculate the units for speed.Circular motion is defined as the movement of an object when its distance from the centre remains constant.The object is rotating in a circle at a constant speed; therefore, when the direction of motion changes, the velocity changes.When a moving object changes direction while maintaining its speed, it experiences a centripetal acceleration (ac), also referred to as a radial acceleration since it acts at right angles to the velocity at any given moment and is directed toward the centre of a circle.The formula for centripetal acceleration is a = v2 / r, where a stands for acceleration, v for velocity, and r for radius. Rearranging terms:
v = sqrt(ra)
v = sqrt( [0.5 m * 8.0 m/sec^2] )
v = sqrt( 4.0 m^2/sec^2 )
v = 2.0 m/sec
The speed of toy train is 2.0 m/sec
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a solenoid is wound with a single layer of insulated copper wire (of diameter 1.0 mm) and is 14.6 cm in diameter and 1.4 m long. how many turns are on the solenoid? assume that adjacent wires touch and that the insulation thickness is negligible.
How many turns are on the solenoid? The number of turns on solenoid are 1.400 turns
To find how many turns on solenoid can be calculated as follows:
Given data,
[tex]d[/tex] (diameter of copper wire) = 1mm = 1×[tex]10^{-3}[/tex]m
[tex]D[/tex] (diameter of solenoid) = 14.6cm = 0.146m
[tex]l[/tex] (length of solenoid) = 1.4m
Next, to determine how many turns on solenoid, we can use the formula below:
[tex]N=\frac{l}{d}[/tex]
[tex]N=\frac{1.4}{0.001}[/tex]
[tex]N=1.400[/tex] turns
Therefore, the number of turns on solenoid are 1.400 turns
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the current in an inductor is changing at 120 a/s and the inductor emf is 51 v. what's the self-inductance?
the self-inductance is 0.425V.s/A
emf = L*di/dt
L = emf/ di/dt = 51/120 = 0.425V.s/A
Self-inductance is a characteristic of the current-carrying coil that opposes or resists changes in the current that passes through it. The self-induced emf generated in the coil itself is mostly responsible for this. Self-inductance is a phenomenon that occurs when a voltage is induced in a current-carrying wire, to put it simply.
When the current increases or drops, the coil's self-induced emf will oppose both movements. Essentially, if the current is increasing, the induced emf's direction is opposite that of the applied voltage, and if the current is decreasing, its direction is similar to that of the applied voltage.
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which is the best reason to use a power model to describe the relationship between the length and period of a pendulum? the standard deviation of the residuals is small.
The reason for using the power model to describe the relationship between the length and the period of the pendulum is because there is a linear relationship between the scatter plots of log (length) vs. log (period of pendulum), but none can be seen in the residual plot.
In the "Power Models" unit, discover which circumstances may be explained by power models, inverse power models, and quadratic models. Additionally, you'll learn how to use the formulae y = ax₂, y = ax₃, y = a/x₂, y = a/x₃, and y = ax₂ + bx + c to compare patterns in tables and graphs of models. Here, x₂ and x₃ are the length of the pendulums at particular instants.
In the framework of these models, they also begin to understand the idea of rate of change. Here, some skills are acquired, like visually solving quadratic equations and simplifying radical and exponential forms. Additionally, direct and inverse variation concepts and phrases are taught.
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a block of mass m starts from rest and slides down a frictionless semi-circular track from a height h as shown below. when it reaches the lowest point of the track, it inelastically collides with a stationary piece of putty also having mass 2m . the block and the putty stick together and continue to slide. what is the maximum height that the block-putty system could reach?
The maximum height of that block-putty system is h/4.
Whtat is inelastic collision?
A collision in which a portion of the kinetic energy of the colliding particles is converted into another type of energy.
What is velocity?
The primary determinant of an object's position and rate of motion is its velocity. It can be explained as the distance an object travels in one unit of time. The object's displacement in a given amount of time is called velocity.
The velocity of block just before hitting the putty (by energy conservation)
K.Ei+P.Ei=K.Ef+P.Ef
⇒0+mgh=21mv2
⇒v=[tex]\sqrt{2}[/tex]gh
Let the common velocity of both block and putty be v'
At collision momentum balance:
mv=mv′+mv′
⇒[tex]\sqrt{2}[/tex]gh=2v′
⇒v′=[tex]\sqrt{g/h}[/tex]
Again applying energy conservation (both block and putty at max height)
K.Ei+P.Ei=K.Ef+P.Ef
⇒1/2 2mv²=2mgh′
⇒1/2 gh/2=gh′
⇒h′=h/4
Therefore, the maximum height is h/4.
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Can a spectrophotometer be used to measure the absorption of a particular wavelength of light that is not visible to the human eye?.
Yes, a spectrophotometer could be used to measure the absorption of a particular wavelength of light that is not visible to a normal human eye.
Although we cannot directly observe the absorption of this light, it is quantifiable. A spectrophotometer, which measures the absorption of light at certain wavelengths (whether visible or not) by a solution, may be used to compute the concentration. The popular and accessible technique of spectrophotometry may be used to determine the concentration of compounds in a solution or the degree of light absorption.
When a light beam is focused through the sample, each component either absorbs or transmits light of a certain wavelength. They are combined with quantifiable and visible colored byproducts. Another is that, as observed by a spectrophotometer, colorless substances generally absorb light from the region of the spectrum that is imperceptible to the human eye.
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in an emergency stop to avoid an accident, a shoulder strap seat belt holds a 60 kg passenger firmly in place. if the car were initially traveling at 90 km/h and came to a stop in 5.5 s along a straight, level road, what was the average force applied to the passenger by the seat belt?
Answer:
272.727N
Explanation:
Force is equal to the product of mass and acceleration. We know the mass of the person (60kg), so we just need to find how much they are decelerating when coming to a stop.
We do this using the motion equation v=u+at, where v is the final velocity, u is initial velocity, a is acceleration, and t is time. Noting 90km/hr=25m/s, we get:
0=25+5.5a
a=-4.5454545m/s^2
Force = mass * acceleration = 60 * 4.545 = 272.727N
the systems shown are in equilibrium. if the spring scales are calibrated in newtons, what do they read?
Newton's first law states that an object at rest will remain at rest, and an object in motion won't change its velocity while the equilibrium condition is met.
When a system is in equilibrium then?When Newton's first law is true, the thing is in its equilibrium condition. When all external forces acting on an object (including moments) are balanced, that object is said to be in equilibrium in the reference coordinate system. This indicates that all external forces and moments acting on this item have a net effect of zero. When an object is at rest or moving with a constant speed in a reference coordinate system, respectively, they are said to be in static equilibrium and dynamic equilibrium.The inertial force produced by the velocity change can be measured by multiplying the mass with the translational acceleration or the mass moment of inertia with the angular acceleration.To Learn more About Newton's first law refer to :
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there are two different objects of different masses. object a has a mass of 50 kgs and object b has a mass of 30kgs. which object will have more inertia and why?
. a car going around a curve of radius r at a speed v experiences a centripetal acceleration ac. what is its acceleration if it goes around a curve of radius 3r at a speed of 2v?
The acceleration of the car that goes around a curve of radius 3r at a speed of 2v is 4 / 3 ( ac )
ac = v² / r
ac = Centripetal acceleration
v = Linear / tangential velocity
r = Radius of curve
This the acceleration of the car that goes around a curve of radius r and velocity v.
For a car that goes around a curve of radius 3r at a speed of 2v,
ac' = ( 2v )² / 3r
ac' = 4v² / 3r
ac' = 4 / 3 ( ac )
Therefore, the acceleration of the car that goes around a curve of radius 3r at a speed of 2v is 4 / 3 ( ac )
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he weight of a body is 50N. how much force is needed to move it vertically upward with 5ms-2 acceleration
5.5 Newton force is needed to move it vertically upward with 5ms-2 acceleration
m=5.1 kg
a= 5m/s²
F=ma
F=5.1×5
F=5.5 N
Every action that attempts to maintain, modify, or change the motion of a body is referred to as a force in mechanics. In his Principia Mathematica, Isaac Newton frequently used his three laws of motion to demonstrate the concept of force (1687).
According to Newton's first law, a body will remain in either its resting or equally moving condition along a straight route in the absence of an external force. The second law states that when an external force acts on a body, the body accelerates (changing velocity) in the direction of the force.
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. an object is placed 53.0 cm in front of a diverging lens. what is the focal length if the distance between object and the image is 30.0 cm?
If there is a distance between the object and the image, the focus length is -0.021cm.
How long is the focal point?A lens's focal length is established when it is focused at infinity. We can determine the magnification—how large individual elements will be—and the angle of view—how much of the scene will be captured—by knowing the focal length of the lens. The narrower the field of view and higher the magnification, the longer the focal length.
Distance from object to picture d= 30 cm.
object distance = 53cm
We must determine the object's distance.
u - v =d
u = 30+53
u = 83cm
We must determine the focus length.
Using the lens
1/f = 1/v -1/u
in the formula, include the value
1/f = 1/-30 -1/83
1/f = -0.021cm
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What wavelength is the maximum absorbance observed in the spectrum displayed in figure 10. 11? report your answer using 3 significant figures.
The spectrum shown has a maximum absorption of 278.4 nm.
The absorbance between 400 and 650 nm is measured, often at intervals of 25 nm, to identify the wavelength of maximum absorption. To identify the wavelength of greatest absorption, the data can be analyzed or graphed.
The useful absorbance range for the majority of spectrometers and colorimeters is between 0.1 and 1. Values of absorbance more than or equal to 1.0 are excessive. Your solution is overly concentrated if the absorbance readings you are getting are 1.0 or higher.
Maximum Absorbance refers to an area with the highest absorbance level. We can infer from the graph that the absorbance is at its highest at wavelength 278.45 nm.
Therefore, maximal absorbance occurs at 278.4 nm wavelength.
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I need help with question 1
Answer:
V = 140 km/h
Explanation:
Velocity is the change in position over time.
We can use the equation V = Δx / t
Note that V is the average velocity.
We are given Δx and t. Lets solve for V.
[tex]V=\frac{540}{4}[/tex]
[tex]V=140[/tex]
[tex]\frac{km}{hour}[/tex]
V = 140 km/h
what is a wavelength? a. The distance from the crest to its neighboring trough in a ways. b. The number of ways in a given period of time. c. The distance between two neighboring troughs in a wave. d. The direction of the wave
Wavelength is (c) the distance between two neighboring troughs in a wave.
What is wavelength?Wavelength is the separation between identical points (adjacent crests) in successive cycles of a waveform signal travelling through space or over a wire. Si unit of wavelength is meter. In wave motion, velocity of wave = wave length × frequency.
Hence, wavelength is a distance between two neighboring identical points such as troughs of a wave. so, option (c) is current answer.
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suppose i produce radio waves with an antenna that have a peak electric field amplitude e and peak magnetic field amplitude b. if i were to double the amplitude of the electric field (i.e. double e) what is the new value for b?
The formula for the relationship between the electric and magnetic fields is:
E = cB
As the amplitude of the electric field is precisely proportional to the magnetic field, the magnetic field will also double in size when the amplitude of the electric field doubles.
Radio waves typically operate at frequencies between 300 gigahertz and below, where the longest wavelengths of the electromagnetic spectrum are found. At 300 GHz, the corresponding wavelength is 1 mm; nevertheless, at 30 Hz, it is 10,000 kilometers.
A magnetic field, a vector field that affects an electric charge, an electric current, and magnetic materials magnetically. In a magnetic field, a moving charge experiences an external force that is perpendicular to the magnetic field and has its own velocity.
The maximum electric and magnetic field strength is known as the amplitude in electromagnetic waves. The wave amplitude determines the energy of the wave. Similar to how waves themselves move, the energy density also follows the electric and magnetic fields.
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in hydrogen fusion, four protons crash into each other to produce a helium nucleus. but the helium nucleus (and other particles created in the reaction, such as neutrinos) is less massive than the protons that form it. what happens to the missing mass?
Missing mass converted into energy.
How does the fusion of four hydrogen atoms into helium atoms occur?Four hydrogen nuclei (photons) combine to form a helium nucleus in the fundamental hydrogen fusion cycle. In the star's core, throughout this fusion cycle, energy is released; in other words, energy is released during this process.
Compared to the original four protons that joined together, the final helium-4 atom weighs less (see E=mc2). Because of this, the mass-energy equivalence of their interaction causes an excess of energy to be released from the Sun as heat and light.
The sun and the stars are propelled by fusion. In one instance of this kind of reaction, two hydrogen atoms combine to create an atom of helium. During the process, a portion of the hydrogen's mass is transformed into energy.
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a car with a mass of 1,020.0 kg accelerates from 0 to 94.0 km/h in 10.0 s. the driver applies the brakes when the car is moving at 94.0 km/h, and the car comes to rest after traveling 38.0 m. what is the net force (in n) on the car during its deceleration? (assume the car is traveling in the positive direction. indicate the direction with the sign of your answer.)
The net force on the car during its deceleration = 9139.2 N
What is deceleration?Deceleration is actually inversely related to acceleration. We know that acceleration is the rate at which an object is speeding up, and deceleration is the rate at which an object is slowing down. For example, when you brake while driving, deceleration is used to slow the vehicle.
Given, m= 1020 kg
u= 0 m/s
V = 94 km/h or 26.1 m/s
t = 10 s
For deceleration
u = 26.1 m/s
v = 0
S = 38 m
by equation of motion ;
v² = u² + 2as
0 = 26.1² + 38a
a = - 8.96 m/s²
Net force during deceleration:
F= m*a
F= 1020 × 8.96
F = 9139.2 N
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If an object accelerates from rest to its final vermouth in 12.3 s what is the final velocity if it traveled 200m
the final velocity is 10.50 m/s.
calculation:
time t= 12.3 s
distance s= 200u=0
equations are, v² = u² + 2as,
s = ut + ½at²
200= 0*12.3 + 1/2*a*
a=2.77
v² = u² + 2as,
v²= 0 + 2*2.77*200
v=10.50 m/s
What is the speed in units?A particle or object's movement with respect to time is expressed vectorially as velocity. The meter per second (m/s), usually referred to as speed, is the accepted unit of velocity magnitude.
In physics, what does "velocity" mean?An object's position and speed are mostly determined by its velocity. It calculates the distance an object travels in a specific length of time. The distance an object travels in a given amount of time is its velocity.
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What are at least two ways that you can get your catapult to increase the horizontal distance of an object launched from it?
Answer:Use Bungee Cord Power. Use the tension of bungee cords as opposed to springs to power your catapult.
Shoot From the Best Angle. Create an arm break that stops the arm at a 45-degree angle from the floor.
Explanation: