v=5at, x=3vt, v=at3x2 and a3=t5x2v are dimensionally consistent.
What does dimensionally consistent means?
Dimensional consistency refers to a property of equations in which the units of all terms are consistent with each other. This means that each term in an equation must have the same units, and the units must be the same as the units of the result. For example, if one term of an equation is a length, all other terms must also have the same unit of length. This ensures that the equation is mathematically valid.
So first we have given there we it equals to this is 5 at. So if we write the dimension or the dimension of the velocity is this is into L t minus one. And The dimension of at will be also this is L into Lt -1. So if you can say that both have the same dimension two dimensionally correct. the dimension of access and and the dimension of well it is so this is also L. So we can see they are dimensionally correct. So we know that the dimension of velocities t minus one. And if we calculate the dimension of this, so the dimension of excess square is early square upon this is it is D cube. So you can see that this is the dimension of execution is L. T -2 into disease D cube. So as we can say that this will comes out and Do You -1. So this is Equals to the LT -1. So this is also dimensionally correct.
Therefore, v=5at, x=3vt, v=at3x2 and a3=t5x2v are the answers.
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A semicircular loop of radius a carries positive charge Q distributed uniformly.(Figure 1) Find the electric field at the loop's center (point P in the figure). Hint: Divide the loop into charge elements dq as shown in the figure, and write dq in terms of the angle d theta, then integrate over theta. Express your answer in terms of i, j, k, Q, a.
The electric field at the center of the charged semicircular loop (point P) is given by: E = (k × Q) / (2 × a) × (i + j + k).
What is electric field?The electric field is a measure of the electric force exerted by a charged object on other charged objects in its vicinity. It is a vector quantity that specifies the direction and magnitude of the force that would be experienced by a unit positive charge placed in that field.
The electric field at the center of a charged circular loop can be calculated using the following steps:
Divide the loop into small charge elements dq, each at an angle dθ from the center of the loop (point P).
The electric field due to each small charge element dq at point P is given by:
dE = (k × dq × r) / (r²),
where k is Coulomb's constant, r is the distance from the charge element dq to point P, and r² = a² + (a × dθ)²
Integrating the above expression over the entire loop (from θ = 0 to θ = π), we get the total electric field at point P:
E = k × Q × (∫(a / (a² + (a × dθ)²) × dθ) from 0 to π)
Evaluating the above integral, we get:
E = (k × Q × a) / (2 × a) = (k × Q) / (2 × a)
Therefore, the electric field at the center of the charged semicircular loop (point P) is given by:
E = (k × Q) / (2 × a) × (i + j + k), where i, j, k are the unit vectors in the x, y, and z directions respectively.
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what is the magnitude of a vertical electric field that will just barely counterbalance the weight of a plastic bead of mass 2.20 g if the bead has been charged to 1.40 μc?
The required magnitude of a vertical electric field that will just barely counterbalance the weight of a plastic bead is calculated to be 15.42 × 10³ C.
The mass of the bead is given as, m = 2.2 g = 2.2 × 10⁻³ kg
The charge on the bead q = 1.4 μc = 1.4 × 10⁻⁶ c
Magnitude of vertical electric field = ?
The electric field's force on the charged plastic sphere equals q E.
The plastic spherical is m g in weight.
where, g is the acceleration due to gravity
Now the force due to electrostatic field is balanced by the weight of the plastic sphere.
q E = m g
E = m g / q
E = (2.2 × 10⁻³)(9.81)/(1.4 × 10⁻⁶) = (2.2 × 9.81 × 10³)/1.4 = 15.42 × 10³ C
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pull the balloon back to about the midpoint between the wall and the sweater. release it again and describe the motion of the balloon using kinematics concepts of velocity and acceleration.
In summation, the balloon's motion may be defined as an entity undergoing steady downward acceleration, with a starting velocity of zero and rising velocity as time passes.
Describe the motion of the balloon using kinematics concepts of velocity and acceleration.The motion of the balloon may be characterized using kinematic principles of velocity and acceleration when it is pushed back to the halfway between the wall and the sweater and then released. The balloon has an initial velocity of zero, v0 = 0, at the instant of release. The gravitational force pressing on it causes it to accelerate downwards. The balloon's acceleration may be described as the acceleration owing to gravity, a = 9.8 m/s2. As time passes, the balloon's velocity rises due to its acceleration. The balloon's velocity may be calculated using the equation v = v0 + at, where t denotes time. The balloon's location may be characterized by the equation x = x0 + v0t + (1/2)at2, where x0 represents the balloon's original position. The balloon's velocity will grow during its travel, reaching its maximum value at the instant it hits its lowest point. Because the balloon is only being affected upon by the constant force of gravity, its acceleration will remain constant.
Here,
In summary, the motion of the balloon can be described as an object undergoing constant acceleration in the downward direction, with an initial velocity of zero and increasing velocity as time progresses.
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A box weighing 43.2 N is pulled horizontally until it slides uniformly over a
level floor. If the applied force is 6.30 N, what is the coefficient of
friction between the box and the floor?
The coefficient of friction between the box and the floor is approximately 0.852.
What do you mean by force?Force is a concept in physics that refers to a push or pull upon an object that results in a change in the object's motion. Forces can cause objects to accelerate, change direction, or change shape. In physics, a force is a vector quantity, meaning it has both magnitude and direction.
Forces can be caused by many factors, including gravity, electromagnetic fields, and the interaction between objects. They can be measured in units of Newtons (N), and the effects of forces can be described by Newton's laws of motion, which explain how objects will respond to different forces.
The coefficient of friction (μ) can be calculated using the formula:
μ = Friction force / Normal force
where the friction force is equal to the applied force minus the force due to gravity on the box:
Friction force = Applied force - Force due to gravity
The force due to gravity on the box is given by:
Force due to gravity = weight of box = 43.2 N
So, substituting these values, we get:
μ = (Applied force - 43.2 N) / 43.2 N
μ = (6.30 N - 43.2 N) / 43.2 N
μ = -36.9 N / 43.2 N
μ = -0.852
Since the coefficient of friction can only be positive, the negative sign indicates that the direction of the friction force is opposite to that of the applied force.
Therefore, the coefficient of friction between the box and the floor is approximately 0.852.
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A 100 g steel ball falls from a height of 1. 8m on to a metal
plate and rebounds to a height of 1. 25 m. Find
a the p. E. Of the ball before the fall (g = 10 m/s2).
bits k. E. As it hits the plate,
cits velocity on hitting the plate,
d its k. E. As it leaves the plate on the rebound,
e its velocity of rebound.
(a) The potential energy of a 100 g steel ball that falls from a height of 1. 8m on to a metal plate and rebounds to a height of 1. 25 m. before the fall = 1.8 Joules
(b) The kinetic energy as it hits the plate = 1.8 Joules
(c) The velocity on hitting the plate = 6 m/s
(d) The kinetic energy as it leaves the plate on the rebound = 5 m/s
To determine the potential energy, use the equation:
PE = mgh
Where:
m = mass of the object (kg)
g = acceleration due to gravity (10 m/s²)
h = height (m)
Hence,
(a)
The potential energy:
PE = mgh
= (0.1) (10) (1.8
= 1.8 Joules
(b)
The kinetic energy as it hits the plate:
KE = PE
KE = 1.8 Joules
(c)
The velocity on hitting the plate:
KE = [tex]\frac{1}{2}[/tex] mv²
1.8 = [tex]\frac{1}{2}[/tex] (0.1)v²
v = 6 m/s
(d)
The kinetic energy as it leaves the plate on the rebound:
PE = mgh
= (0.1) (10) (1.25)
= 1.25
KE = [tex]\frac{1}{2}[/tex] mv²
1.25 = [tex]\frac{1}{2}[/tex] (0.1) v²
v = 5 m/s
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An object has a charge of -1.6x10-13C, and object B is electrically neutral. Two million electrons are removed from A and placed on B. Expressed in coulombs, what is the resulting charge (algebraic sign and magnitude) on A and on B? (step by step explanation please)
The resulting charge on A is [tex]1.6 x 10^-7[/tex] C, and the resulting charge on B is [tex]-3.2 x 10^-7[/tex] C.
What do you mean by charge?A charge is a property of matter that results from the presence or absence of electrons. It can be either positive or negative, and two objects with opposite charges will be attracted to each other, while two objects with the same charge will repel each other. The unit of charge is the Coulomb (C), which is defined as the amount of charge carried by 6.242 x 10^18 electrons. The concept of charge is important in many areas of physics, including electricity and magnetism, and plays a role in many natural phenomena and technological applications.
The charge on object A is [tex]-1.6 X10^-13[/tex]C.
When two million electrons are removed from object A, the charge on object A becomes more negative. The charge on object A can be calculated using the formula:
Q = Q - ne,
where Q is the original charge, n is the number of electrons, and e is the charge of an electron, which is -1.6 x 10^-19 C.
Therefore, the charge on object A becomes:
[tex]Q = -1.6 X 10^-13 C - (2X10^6)(-1.6X 10^-19 C)[/tex]
[tex]= -1.6 X 10^-13 C + 3.2X 10^-7 C[/tex]
= 1.6 x 10^-7 C
Object B starts as electrically neutral, which means that the total charge on B is 0 C. When two million electrons are placed on object B, the charge on object B becomes more negative. The charge on object B can be calculated using the formula:
Q = Q + ne,
where Q is the original charge, n is the number of electrons, and e is the charge of an electron, which is -1.6 x 10^-19 C.
Therefore, the charge on object B becomes:
Q = 0 C + (2 x 10^6)(-1.6 x 10^-19 C)
[tex]= -3.2 X 10^-7 C.[/tex]
So, the resulting charge on A is[tex]1.6 X 10^-7[/tex]C, and the resulting charge on B is [tex]-3.2X 10^-7[/tex] C.
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a student must conduct an experiment in which an elastic collision occurs. in the experiment, block x of mass 2kg travels with a velocity vx in the positive direction toward block y of mass 2kg that is at rest, as shown in figure 1. after the collision, block y travels in the positive direction with velocity vy while block x remains nearly at rest. data collected of the initial and final velocities of both blocks for three trials of the experiment are shown in the table. did the student conduct an experiment in which an elastic collision occurred? is the system of block x and block y open or closed?
Yes, the student conducted an experiment in which an elastic collision occurred. The system of block x and block y is a closed system.
What is closed system?
A closed system is a system where the components are isolated from the environment. This type of system does not allow any kind of exchange of energy, matter, or information with the environment.
This means that the system is in a state of equilibrium, where the total energy and matter is conserved, and the system is not affected by any external influences.
Therefore, Yes, the student conducted an experiment in which an elastic collision occurred. The system of block x and block y is a closed system.
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i need help on this please answer rrght away!
Measurement that is used to record the heat transfer of a solution in a classroom investigation.
The most common measurement used to record heat transfer in a classroom investigation is a calorimeter.
A calorimeter is a device used to measure the amount of heat transferred to or from a substance during a chemical or physical reaction. It is commonly used in the classroom setting for experiments that involve the transfer of heat energy. The basic design of a calorimeter consists of an insulated container that holds the substance and a thermometer or temperature probe to measure the temperature change of the substance.
The insulation helps to reduce heat loss to the surrounding environment, which makes the measurement of heat transfer more accurate. Calorimeters can be used to determine the specific heat capacity of a substance, to measure the heat of reaction in a chemical reaction, or to measure the heat transfer between two substances of different temperatures. The results of these experiments can be used to calculate the amount of energy transferred and to determine the energy changes that occur during chemical reactions.
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answer this question al six marks please my slays
Answer:
the driver need to stop before he drive
Explanation:
if he keep driving he will hit a car
an object of mass 1 kg that is moving in a straight line on a level surface slows down from 4 m/s to rest. what is the net work done on the object?
Net work done on the object -16J.
Net work done on the object = Force x Distance
Force = mass x acceleration = 1 kg x (-4 m/s) = -4 N
Distance = Change in velocity x time = (4 m/s - 0 m/s) x 1 s = 4 m
Net work done on the object = Force x Distance
= -4 N x 4 m
= -16 J
What is work done?
Work done is the amount of energy expended to move an object a certain distance. It is calculated by multiplying the force applied to the object by the distance it is moved. Work is measured in Joules (J).
Therefore, Net work done on the object -16J.
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a 65- kg person is skiing down a hill. the skier’s speed at the bottom is 15 m/s. if the skier hits a snowdrift and stops in 0.30 s, (a) how far does she go into the drift? (b) with whay average force will she strike the drift?
If the skier hits a snowdrift and stops in 0.30 s, She would go into the drift to 2.25 m. The average force that she will strike the drift is 3250 N.
What is speed?The speed at which an object's location changes in any direction. The distance traveled in relation to the time it took to travel that distance is how speed is defined.
a = -15 / 0.3 = -50 m/s2
v2 - v02 = 2ax
- 152(-50)x == > x = 2.25 m
F = ma = 65 x 50 = 3250 N
Therefore, a. She would go into the drift to 2.25 m.
b. The average force that she will strike the drift is 3250 N.
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a 100-cm -thick layer of oil floats on a 170-cm -thick layer of water. what is the pressure at the bottom of the water layer?
The pressure at the bottom of the 170-cm-thick water layer is 17,000 Pa.
The pressure at the bottom of the water layer can be calculated using the formula for pressure due to a fluid column:
P = ρgh
where P is the pressure, ρ is the density of the fluid, g is the acceleration due to gravity, and h is the height of the fluid column.
Since water has a density of about 1000 kg/m^3, the pressure at the bottom of the 170-cm-thick water layer is given by:
P = 1000 kg/m^3 * 9.8 m/s^2 * (170 cm / 100 cm/m)
P = 17,000 Pa
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which of jupiter's moons was found to have active volcanoes on it?
The stony moon of Jupiter With hundreds of eruptions, some of which are spouting lava fountains that are a few kilometers (or kilometers) high, Io is the solar system's largest volcanically active planet.
What makes Jupiter so distinctive?By far the biggest world in the solar system, Jupiter is more than times as large than all of the other planet put altogether. Jupiter is the sixth planet from our Sun. The swirls and patterns of Jupiter are really urea and water clouds floating in a helium- and hydrogen-rich atmosphere.
Jupiter has to be either hot or cool.The clouds tops are thought to be roughly -280 degrees Fahrenheit frigid. The overall temperature of Mars is -238 degrees Fahrenheit. Jupiter's pole is only little more than 3 degrees inclined, therefore
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why should the wavelength scale of spectroscope be calibrated
Your spectroscope must be calibrated in order to account for systematic inaccuracy. The helium discharge tube is a handy source of emission lines.
Why is it necessary to calibrate the spectroscope's wavelength?Spectrometers will inevitably drift over time as a result of impacts and effects from the environment. Regular wavelength calibration, which helps to assure accurate and dependable spectroscopic data, can readily address this prevalent problem. The wavelength calibration verifies that the grating's angular position setting and the wavelengths assigned to each pixel on the CCD array detector are correct. By analysing the spectra of an orange glass and a suspension of microalgae, the process is demonstrated.
This is accomplished by comparing the wavelengths you empirically determined to wavelengths discovered via research in the literature.
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how many degrees are there on both the celsius and kelvin temperature scales, between the normal freezing and boiling points of water?
On both the the celsius and kelvin temperature scales, 100 degrees is the difference between normal freezing and boiling points of water.
Boiling point
The temperature at which a fluid bubbles and goes to fume for example significantly alters its state at climatic strain is known as the edge of boiling over of the fluid.
Bubbling is a mass peculiarity.Edge of boiling over of waterThe edge of boiling over of water is the edge of boiling over of water fluctuates with air pressure.We know that on celsius scale,freezing temperature of water is =0°C
and,boiling point of water is =100°C
Similarly,freezing point of water in kelvin scale=273K
and boiling point of water in kelvin scale=373K.
So,difference between normal freezing point of water and boiling point of water=100-0=100°C
Hence,difference is of 100°C in both kelvin and degree scale.
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A string is stretched between two clamps held 4.02 m apart. The string is made to oscillate at its third harmonic frequency.
Calculate the distance in m between two adjacent nodes to.
The distance between two adjacent nodes of the wave is determined as 8.04 m.
What is the distance between two adjacent node?
The distance between two adjacent nodes of the wave is calculated by applying the following formula;
Node to Node = λ/2
Node to Node = length of the string = 4.02 m
where;
λ is the wavelength of the wave or the distance between two adjacent nodesThe distance between two adjacent nodes of the wave is calculated as;
λ/2 = L
λ = 2L
λ = ( 2 ) x ( 4.02 m )
λ = 8.04 m
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which of the following statements accurately represents the relationship between linear and angular motion? none of the answers are correct. linear motion of joints produces an angular motion. angular motion of joints produces the linear motion of walking, and linear motion of joints produces an angular motion. angular motion of joints produces the linear motion of walking.
The correct statement is: Angular motion of joints produces the linear motion of walking.
Angular motion is the motion of a body about a fixed point or fixed axis. It is equal to the angle passed over at the point or axis by a line drawn to the body.Relationship between linear and angular motion are as follows:Displacement – In linear motion, we use ‘s’ to quantify the linear distance travelled. In angular motion, we use ‘θ’ for the same to quantify the angular distance, and it is measured in radians.
Velocity – In linear motion, we use ‘v’ to denote velocity while in angular motion, we use ‘ω’ to indicate angular velocity. Angular velocity is the number of radians covered per second.
Acceleration – We use ‘a’ to denote linear acceleration, while we use ‘α’ to mean angular acceleration. The unit of angular acceleration is radians per second square
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a bicyclist moving at a speed of 15.0 m/s rounds a bend with a radius of 28.0 m. what is the centripetal acceleration of the cyclist?
Centripetal acceleration of the cyclist is 8.04 m/s^2, while the moving speed of the cyclist is 15.0m/s.
The centripetal acceleration of an object moving in a circle with a radius "r" and velocity "v" can be calculated using the following formula:
a = v^2 / r
where "a" is the centripetal acceleration.
Given the speed of the cyclist
(v) = 15.0 m/s and
the radius of the bend (r) = 28.0 m,
the centripetal acceleration can be calculated as follows:
= a
= v^2 / r
= (15.0 m/s)^2 / 28.0 m
= 225 m^2/s^2 / 28 m
= 8.04 m/s^2
So the centripetal acceleration of the cyclist is 8.04 m/s^2.
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the pressure of the helium inside a toy balloon is 1250 mm hg. what is this pressure in kpa?
The pressure of the helium inside a toy balloon in kpa is calculated to be 166770 kPa.
Pressure of helium = 1250 mm Hg
Converting into m Hg, we have,
p he = 1250/1000 = 1.25 m Hg
From the physical properties of Hg, we know,
ρ Hg = 13.6 g/cm³ = 13600 kg/m³
Gravity of the earth = 9.8 m/s²
The helium pressure inside a toy balloon is, in kPa,
p he = ρ g h = 13600 ×9.81 × 1.25 = 166770 kPa
Thus, the required pressure of the helium inside a toy balloon in kpa is calculated to be 166770 kPa.
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what's the mass of the Sun?
Volume and mass The sun has a total volume of 1.4 x 10 28 cubic meters. According to NASA data, 1.3 million Earths might fit inside the sun.
How does physics define mass?
It is the most fundamental characteristic of matter and one of the basic quantities in physics. Mass is a term used to describe how much matter is there in a body. The kilogram is the SI mass unit. (kg). A body's mass does not alter at any point in time. only in rare instances where a significant quantity of energy is supplied to or taken away from a body.
How is mass determined?
Mass can be calculated using the formula: mass = volume density. Weight serves as a gauge for gravitational force.
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Three identical container P, Q and R are taken, and kept - one on the terrace of a tall building; another on the terrace of a horter building; and the third in an open pace. After a rain, which one will have the highet level of water, auming no overflow and no obtruction near the container?
The container kept on the terrace of the taller building will have the highest level of water.
What is atmospheric pressure ?The level of water in a container depends on atmospheric pressure, and the atmospheric pressure decreases with height.
Atmospheric pressure, also known as air pressure, is the force exerted by the weight of air molecules in the atmosphere. It is measured in units of force per unit of area, typically in kilopascals (kPa) or pounds per square inch (psi).
Atmospheric pressure decreases with increasing altitude, as there are fewer air molecules above the earth's surface. At sea level, the average atmospheric pressure is approximately 101.3 kPa (14.7 psi), while at high elevations it can be significantly lower.
The taller building is higher up, so the atmospheric pressure on its terrace is lower than that at ground level, resulting in a lower water level in the container kept there.
The water level in the container kept on the terrace of the shorter building and the one kept in an open space will be at the same height, as they are both at ground level and have the same atmospheric pressure.
Therefore, The container kept on the terrace of the taller building will have the highest level of water.
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what is the time for one cycle of the radio wave?
A radio wave's frequency is the number of cycles it completes in one second, and is measured in hertz (Hz).
One cycle of a radio wave is the time it takes for the wave to complete a cycle of its waveform, from the peak to the trough, and back to the peak again. A radio wave's frequency is the number of cycles it completes in one second, and is measured in hertz (Hz). For example, a radio wave with a frequency of 1 MHz (one million hertz) will have a cycle time of 1 microsecond (one millionth of a second).
The cycle time of a radio wave is the inverse of its frequency, and represents the time it takes for the wave to complete one full cycle of its waveform, from peak to trough and back to peak again. The higher the frequency, the shorter the cycle time, and vice versa.
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draw x−t graph for the motion of the bumper between t=0 and t=2.00s .
The graph of x-t for the motion of the bumper between t=0 and t=2.00s is a straight line that starts at the origin (x = 0, t = 0) and ends at (x = 2, t = 2). This shows that the bumper moves with a constant speed of 2 m/s.
What is the graph ?A graph is a visual representation of data or information. It typically includes a set of points that are connected by lines or curves to form a picture. Graphs are used to easily visualize trends, compare values, and show relationships between different data sets. They provide an effective way to communicate information to a wide range of audiences. Graphs can be used to illustrate almost any type of data, from population trends to stock market fluctuations.
This graph can be interpreted as follows: the bumper starts from rest (x = 0) at t = 0 and travels a distance of 2 meters in 2 seconds, meaning it has a constant velocity of 2 m/s. The slope of the line is equal to the velocity of the bumper, so m = 2 m/s. This means that for every 1 second that passes, the bumper moves 2 meters.
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How long does it take for radio signals to travel from Earth?
The time it takes for radio signals to travel from Earth depends upon the distance they are traveling to. Radio signals travel at the speed of light, which is roughly 299,792,458 meters each second.
In this way, to compute the time it would take for a radio transmission to travel a specific distance, you would isolate the distance by the speed of light which is about 3 x 108 m/s
For example, if the radio transmission is traveling to a planet that is 40 million kilometers away, it would require the radio transmission roughly 133.3 seconds to arrive.
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two point charges of 30 μc each are 4 cm apart. what is the electric field at the midpoint between the two charges?
The electric field at the midpoint between the two charges each of 30 μC, is zero.
Charge q₁ = +30 μC
Charge q₂ = +30 μC
Distance between both the charges, d = 4 cm
Midpoint will be 2 cm from each charge. so r = 2 cm
We know the electric filed produced by a charge, at a distance of d is formulated as, E = q/(4πε₀r²)
Where q is the charge, ε₀ is the constant of permittivity of vacuum.
Let 1/(4πε₀) = k, then E = kq/r²
Electric field due to first charge at 2 cm from it, E₁ = (k × 30)/2²
Similarly, electric field due to second charge at 2 cm from it, E₂ = (k × 30)/2²
E = E₁ - E₂
E = (k × 30)/2² - (k × 30)/2²
E = 0
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Determine the required concentration (in percent by mass) for an aqueous ethylene glycol (C2H6O2) solution to have a boiling point of 108.3 ∘C. Express your answer using two significant figures. nothing % %
The required concentration (in percent by mass) for an aqueous ethylene glycol (C2H6O2) solution is 51 %.
What is Ethylene glycol?A helpful industrial substance called ethylene glycol can be found in a variety of consumer goods. Antifreeze, some stamp pad inks, ballpoint pens, solvents, paints, plastics, films, and cosmetics are a few examples. It may also serve as a delivery system for drugs.
Because of its pleasant flavor, ethanol is frequently consumed intentionally or by mistake. In the body, ethylene glycol decomposes into harmful substances.
The central nervous system (CNS), followed by the heart and kidneys, are the first organs that are impacted by ethylene glycol and its harmful byproducts.
Therefore, The required concentration (in percent by mass) for an aqueous ethylene glycol (C2H6O2) solution is 51 %.
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An elevator is moving upward and speeding up. What is the sign of the work done by the force of gravity acting on the elevator? A) positive B) Negative C) Zero D) this question cannot be answered without knowing the direction of the elevator's acceleration.
The downward force caused by gravity will be the same as the normal force, that is the power of the elevators on this child's shoes. So, 98 newtons will be the typical force in this situation.
What does force in physics mean?
You can also use words like stretch and compress to describe force. Force is described in physics as the pull or push that causes a massed object to change its speed. Force is an outside agent that has the power to alter a body's resting or moving position.
What is a good instance of force?
When applied, force is an outside factor that modifies or tends to modifies a body's condition; if indeed the body is moving
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a particle moves along a straight line with equation of motion s = f(t), where s is measured in meters and t in seconds. find the velocity and speed when t = 9.
The value of velocity at t = 9 when the equation of motion is given is calculated to be -1.0123.
The given function is f(t) = (t^-1) - t, it is an equation of motion.
On derivation of the equation of motion, we get the equation of velocity.
Taking derivative on both the sides of the function,
f'(t) = d/dt[(t^-1) - t)] = d/dt(t^-1) - d/dt(t)
f'(t) = -1(t^-2) -1
f'(t) = -t^-2 - 1
f'(t) = v(t),
It can be also written as,
-1/t^2 - 1
To find out the velocity at t = 9, place the value in the above equation.
So, v(9) = -1/(9^2) - 1 = -1/81 - 1 = -0.0123-1 = -1.0123
The given question is incomplete. The complete question contains 'f(t) = (t ^-1) - t.'
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What is the speed of the lander just before it touches the surface? the acceleration due to gravity on the moon is 1. 6 m/s2.
The speed of the lander just before it touches the surface will be the highest it has been during its descent.
The speed of the lander just before it touches the surface can be calculated using the equation: v = √(2gh), where g is the acceleration due to gravity on the moon (1.6 m/s^2), h is the height above the surface, and v is the velocity.
Assuming h is a constant value, the velocity of the lander can be calculated as the square root of two times the acceleration due to gravity multiplied by the height. This equation is known as the equation of motion and is used to calculate the velocity of an object in free fall. It is important to note that the velocity will increase as the height decreases, so the speed of the lander just before it touches the surface will be the highest it has been during its descent.
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