You have a remote-controlled car that has been programmed to have velocity v⃗ =(−3ti^+2t2j^)m/s, where t is in s. At t = 0 s, the car is at r⃗ 0=(3.0i^+2.0j^)m.
What is the y component of the car's position vector at 8.0 s ?
What is the x component of the car's acceleration vector at 8.0 s ?
What is the y component of the car's acceleration vector at 8.0 s ?

Answer: a AND B

Explanation:1, IS TRUE AND 2 AIS TRUE

The things that are true about a system are :

A system is a group of objects analyzed as one unit

Energy that moves across the system boundaries is conserved.

System is nothing more than a group of identifiable items (or smaller systems), as it is defined in physics or chemistry. The word "system" often refers to a collection that makes it easier to think about an issue. Everything else outside of what the system defines is considered the surrounds.

The collection of elements and energy under study is referred to as a system. For instance, everything within a jar in which reactions are taking place is the system, while everything outside the jar is the environment. Everything outside of the system, or the rest of the cosmos, is considered the surrounds.

The things that are true about a system are :

A system is a group of objects analyzed as one unit

Energy that moves across the system boundaries is conserved.

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Neglecting the effects of air resistance, the statement that is true about a freely falling rock is the one that says "the rock will gain an equal amount of momentum during each second (of its fall)." Therefore, the correct answer is option A.

According to the question, a rock is dropped from a tower. It falls freely, meaning that there is no initial force that was applied to it and that the falling is purely under the influence of gravity. In cases like this, the primary force that is working on the rock, besides gravity, is the friction that it experiences with the air (air resistance).

Falling objects get faster the longer they are in the air because of the momentum it gains. Air resistance slightly slows the speed, but since we're instructed to ignore the air resistance, only the acceleration of gravity would affect the object.

The formula you can use to calculate a falling object is:

  v = g * t

  v = 2 * g * h

  h = 0.5 * g * t²

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The following statement which is true is :  A correlation of .33 is just as strong as a correlation of -.33.

The tendency of two or more systems that independently exhibit simple behavior to show complex and novel behavior together because of their interaction is called correlation.

Correlation is a statistical measure that expresses extent to which two variables are linearly related implying that they change together at a constant rate. It is common tool for describing simple relationships without making statement about cause and effect.

Correlation between variables does not mean that the change in one variable is the cause of the change in the values of other variable.

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The equation of motion can be written as dv/dt = (49² - v²)/245. And its explanation is given below.

The mass of the object is given 1 kg.

Let us write the differential equation of a falling object that falls under influence of the drag force described.

dv/dt = mg - cv² = 9.8 - cv²

Now, we will determine the drag coefficient c by using limiting velocity.

The limiting velocity is also an equilibrium. So, we can determine it by substituting dv/dt = 0 and v = 49 m/s

0 = 9.8 - c 49²

c = 9.8/49² = 1/245

Hence, initial differential equation can be written as,

dv/dt = 9.8 - v²/245 = (49² - v²)/245  

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The speed of the bullet is 2.595 m/s m/s.

Generally, The speed of the bullet can be determined using the formula:

v = (2 * π * r * n * θ) / 360

where:

First, we need to convert the rotational speed from rev/min to rev/s:

n = 545 rev/min * (1 min / 60 s)

= 9.08 rev/s

Next, we need to convert the radius of the disk from cm to m:

r = 65 cm * (1 m / 100 cm)

= 0.65 m

Finally, we can plug in the values and solve for the speed:

v = (2 * π * 0.65 * 9.08 * 25.2) / 360

v= 2.595 m/s

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A closed system is a system in which the total energy of the system is conserved.

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Formula for work:

[tex]w=Fd[/tex]

work(measured in joules) = force(measured in newtons) * distance(measured in meters)

Formula for force:

[tex]F=ma[/tex]

force(measured in newtons) = mass(measured in kilograms) * acceleration(measured in m/s^2)

__________________________________________________________

Given:

[tex]m=60kg[/tex]

[tex]d=10m[/tex]

[tex]a=9.8m/s^2[/tex]

[tex]w=?[/tex]

__________________________________________________________

Finding force:

[tex]F=ma[/tex]

[tex]F=60\times9.8[/tex]

[tex]F=588N[/tex]

__________________________________________________________

Finding work:

[tex]w=Fd[/tex]

[tex]w=588\times10[/tex]

__________________________________________________________

Answer:

[tex]\fbox{w = 5880 Joules}[/tex]

between the moment the driver sights an obstacle and the moment he applies the brakes

What is a driver’s response time?

A driver’s reaction time is the amount of time it takes between seeing an obstruction and applying the brakes. During this period, the automobile maintains a steady speed while he drives closer to the obstruction. The reaction time is the amount of time it takes to respond to a situation by shifting your foot from the accelerator to the brake pedal. A typical reaction time is ¾ of a second. The reaction distance is the distance traveled by a vehicle within this period.

Method that is more exact.D = (s * r) / 3.6 d = response distance in meters (to be calculated). S denotes the speed in kilometers per hour. R denotes the response time in seconds. 3.6 = fixed conversion figure

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Kepler's second law states that as a planet orbits the Sun, it sweeps out equal areas in equal times. the options are b) Inner planets orbit the Sun at higher speed than outer planets, d) All the planets orbit the Sun in nearly the same plane, f) Pluto moves faster when it is closer to the Sun than when it is farther from the Sun.

Kepler's second law states that as a planet orbits the Sun, it sweeps out equal areas in equal times. The following statements describe characteristics of the solar system that are explained by Kepler's second law:

The correct options are option b, d and f.

These statements are consistent with the idea that a planet sweeps out equal areas in equal times as it orbits the Sun, because a planet moving faster would be able to sweep out a larger area in a given amount of time. Kepler law is made to find the distance, motion, trajectory of the celestial bodies that are moving in he solar system and we can use it to prove many theories and we are making the proportionality in the many ways.

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The difference in magnitude of the two stars where one star has 15.8 times more flux than the other star is 2.975.

Luminosity of a star is the rate at which the star radiates energy into the space. Apparent brightness is the rate at which a star's radiated energy into the space reaches an observer on the Earth. Apparent brightness depends on both the luminosity of the star and distance from the star.

m₂ - m₁ = -2.5 log (I₂/ I₁)

m₂ - m₁ = -2.5 log (1/ 15.8)

m₂ - m₁ = -2.5(log 1 - log 15.8)

m₂ - m₁ = -2.5 (0 - 1.19)

m₂ - m₁ = -2.5 (-1.19)

m₂ - m₁ = -2.5 × -1.19

m₂ - m₁ = 2.975

Therefore, the difference in magnitude of the two stars is 2.975.

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Answer:

a) To find the depth of the lake, we can use the following equation:

distance = initial velocity x time + (1/2) x acceleration x time^2

As the ball sinks to the bottom with the same constant velocity, we can assume that the acceleration is due to gravity, which is 9.8 m/s^2 (going downward)

We know that the time it takes for the ball to hit the bottom is 5.05 seconds, so we can substitute these values into the equation:

distance = 0 x 5.05 s + (1/2) x 9.8 m/s^2 x (5.05 s)^2

distance = 12.6125 m

So the lake is 12.6125 m deep

b) To find the magnitude of the average velocity of the ball for the entire fall, we can use the equation:

average velocity = distance / time

We know that the distance is the depth of the lake, which is 12.6125 m, and the time is 5.05 s, so we can substitute these values into the equation:

average velocity = 12.6125 m / 5.05 s

average velocity = 2.49 m/s

c) To find the magnitude of the initial velocity of the ball when it is thrown, we can use the following equation:

initial velocity = final velocity^2 + 2 x acceleration x distance

As the ball reaches the bottom in the same time as when it was dropped, 5.05 s, we can assume that the final velocity is 0 m/s. We know that the acceleration is 9.8 m/s^2 (going downward), and the distance is the depth of the lake, which is 12.6125 m. So we can substitute these values into the equation:

initial velocity = 0^2 + 2 x 9.8 m/s^2 x 12.6125 m

initial velocity = 24.6 m/s

Note that the magnitude of initial velocity is 24.6 m/s, which is a scalar value, it doesn't have any direction.

The time period of simple pendulum in which g is constant l is length of pendulum is T=2pirootl/g which oscillates with a period of 2 ss.

a- for a simple pendulum force constant or spring factor k is proportional to mass m therefore m cancels out in denominator as well as in numerator.

b-in case of a simple pendulum the restoring force acting on the bob of the pendulum is given as:-

F=-mgsing theta

m=mass of bob

g= acceleration due to gravity

theta=angle of displacement

for small theta sintheta =theta

hence time period T=2pirootL/g.

A simple pendulum is a point mass suspended by a weightless and inextensible string fixed rigidly to support, the supported string and mass is called pendulumn.

T = 2π√(l/g)

l is the length of the pendulum.

g is the acceleration due to gravity.

Examples of simple pendulums are found in clocks, swing sets, and even the natural mechanics of swinging legs all are on the basis of simple pendulum. Tetherballs are examples of spherical pendulums.

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Light travels at a speed of approximately 300,000 km/s, so it takes 1.28 seconds for light to travel from the Moon to the Earth at a distance of 384,000 km.

The process of light traveling from the Moon to the Earth is a simple one. As it travels, the light waves spread out and become weaker, but they still reach the Earth in 1.28 seconds, as they have traveled a distance of 384,000 km.

Light is a form of energy, and it is made up of tiny particles called photons. As photons travel through space, they interact with various objects and obstacles, such as planets and stars, and this causes them to lose energy. This is why the light from the Moon becomes weaker as it travels to the Earth.

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One cubic meter of water has a mass of 1000 kilograms,

since[tex]1 m^3 = 1000 L[/tex] and 1 kilogram is equal to 1000 grams.

Since the gram was initially defined as the mass of one cubic centimetre of water at its greatest density at 4 °C, the density of water is around [tex]1 g/cm^3[/tex].

One cubic centimetre equals one millilitre of volume. One cubic centimetre of water has a mass of approximately one gram at 3.98 °C (the temperature at which it reaches its greatest density).

To convert cubic centimeters to cubic meters, divide by 1000000 or multiply by 0.000001. A typical volume unit conversion is from cubic centimeters to cubic meters ([tex]cm^3 \:to \:m^3[/tex]).

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The momentum of the red cart before and after the collision is 60 kgm/s and 40 kgm/s respectively.

The momentum of the blue cart before and after the collision is 30 kgm/s and 50 kgm/s respectively.

The final momentum of the carts after the collision is determined by applying the principle of conservation of linear momentum.

Sum of initial momentum = sum of final momentum

60 kgm/s  +  30 kg m/s  = 50 kgm/s  + Pr

where;

90 kgm/s - 50 kgm/s = Pr

40 kgm/s = Pr

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A straight line drawn anywhere on a Mercator projection is a line of true compass direction, called a loxodrome line.

A loxodrome is a line of true compass direction on a Mercator projection map. Here are some key points to keep in mind:

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Answer:

the velocity when the displacement is zero is 17.95 m/s.

Explanation:

The initial velocity can be found by taking the first derivative of the position function (s) with respect to time (t). The velocity function v = ds/dt is given by:

v = 8 * 2t + 3

The initial velocity, v0, at t = 0, is:

v0 = 8 * 2 * 0 + 3 = 3 m/s

The velocity when the displacement is zero can be found by setting s = 0 in the position function and solving for t:

0 = 8t² + 3t - 10

Using the quadratic formula, we find that:

t = (-3 ± √(3² - 4 * 8 * -10)) / (2 * 8)

t = (-3 ± √(9 + 320)) / 16

t = (-3 ± √329) / 16

t = (-3 ± 18.12) / 16

t = (15.12 / 16) or (-21.12 / 16)

Since time cannot be negative, we take the positive value:

t = (15.12 / 16) = 0.9475 s

At t = 0.9475 s, the velocity can be found using the velocity function:

v = 8 * 2 * 0.9475 + 3 = 17.95 m/s

So, the velocity when the displacement is zero is 17.95 m/s.

Answer:

The more mass an object has, the more gravitational acceleration it will experience

Explanation:

So when we talk about gravitational mass, we're talking about how much an object is affected by gravity. And the correct statement is:The more mass an object has, the more gravitational acceleration it will experience.Think about it like this: a heavy bowling ball will be pulled down harder by gravity than a light tennis ball. The heavy bowling ball has more mass, so it experiences more gravitational acceleration. Make sense?

The gravitational mass is directly proportional to the acceleration of the object. The more mass an object has, the more gravitational acceleration it will experience. Thus, the correct option is B.

Gravitational mass is the charge to which the gravity couples. Inertial mass can be defined as a measure of how fast an object accelerates in the given same force, increasing the inertial mass implies the decreasing acceleration.

The gravitational acceleration of an object is the acceleration of an object which the mass experiences due to the impact of force of gravity on the object.

Gravitational mass is a gravitational force which is present between any pair of given objects, which is given by the formula:

F = Gm₁m₂/ r²

where, G is the universal gravitational constant, m₁ and m₂ are the masses of the two objects, and r is the distance between them.

Therefore, the correct option is B.

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Answer:very hard

Explanation:

Answer:

31.37 degree Celcius

Explanation:

To calculate the final steady temperature of the mixture, we need to use the conservation of energy principle, which states that the total energy before and after the process must be the same. The heat lost by the copper block will be equal to the heat gained by the water and the copper calorimeter.

We can start by finding the heat lost by the copper block. We know that the mass of the copper block is 24 grams, and the specific heat capacity of copper is 400 J/kg·K.

The change in temperature of the copper block is 230°C - 31°C = 199°C. Therefore, the heat lost by the copper block can be calculated as:

Q_copper = mass x specific heat capacity x change in temperature

Q_copper = (24 g) x (400 J/kg·K) x (199°C)

Q_copper = 150336 J

Next, we'll find the heat gained by the water and the calorimeter. We know that the mass of the water is 54 grams, and the specific heat capacity of water is 4200 J/kg·K.

The change in temperature of the water is T_final - 31°C = T_final - 31. Therefore, the heat gained by the water can be calculated as:

Q_water = mass x specific heat capacity x change in temperature

Q_water = (54 g) x (4200 J/kg·K) x (T_final - 31)

We also know that the mass of the calorimeter is 60 grams, and the specific heat capacity of copper is 400 J/kg·K.

The change in temperature of the calorimeter is T_final - 31°C = T_final - 31.

Therefore, the heat gained by the calorimeter can be calculated as:

Q_calorimeter = mass x specific heat capacity x change in temperature

Q_calorimeter = (60 g) x (400 J/kg·K) x (T_final - 31)

Now we can use the conservation of energy principle to find the final steady temperature. Since the heat lost by the copper block is equal to the heat gained by the water and the calorimeter, we can set up the following equation:

Q_copper = Q_water + Q_calorimeter

150336 J = (54 g) x (4200 J/kg·K) x (T_final - 31) + (60 g) x (400 J/kg·K) x (T_final - 31)

Solving for T_final, we get

T_final = (150336 J + 31*(544200 + 60400))/(544200+60400)

= (150336+31*266400)/266400

= (150336+828240)/266400

= 98576/266400

= 0.37°C

Therefore, the final steady temperature of the mixture is T_final = 31°C + 0.37°C

= 31.37°C

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Answer: Can be larger or smaller than each individual force, depending on the directions, they are acting in.

Is the overall effect of all the forces acting on an object.

Explanation:

Net force can be larger or smaller than each individual force, depending on the directions they are acting in is the overall effect of all the forces acting on an object is the sum of all the forces acting on an object except gravity.

The net force is the combined effect of all the pushing and pulling forces acting on the object. If the forces pushing or pulling on an object are not balanced then the object will accelerate in the direction of the net force.

The net force is the resultant force of all the individual applied forces. So, the force is either larger or smaller than individual forces, because force is a vector quantity.

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The correct sequence is 5, 1, 3, 8, 4, 6, 7, 2. The statement that is being discussed is:

"For all > 0 there exists a > 0 such that for all satisfying we have that ."

To explain the statement further, it means that for any given real number > 0, there exists a real number > 0 such that for all real numbers satisfying , we have that . In other words, if is sufficiently close to (i.e. if is less than ), then must also be close to (i.e. must be less than ).

This idea is essential to understanding limits. The statement can be written more formally as:

[tex]$$\lim_{x \to c} f(x) = L \iff \forall \epsilon > 0, \exists \delta > 0 \text{ such that } \forall x \in \mathbb{R}, 0 < |x - c| < \delta \Rightarrow |f(x) - L| < \epsilon$$[/tex]

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The images sharpen when the goggles are worn because the focal length of goggles maintains the refraction of light into cornea and corrects the vision of the swimmer.

What is Refraction?

Refraction is the redirection of a wave as it travels through one medium and into another in physics. The wave's alteration in speed or a change in the medium might both result in the redirection. Although light refraction is the most frequently seen phenomena, refraction can also occur with other waves, including sound and water waves.

The angle between the original direction of wave propagation and the direction of speed change affects how much a wave is refracted. Light slows down and somewhat changes direction as it moves from the air into the water. Refraction describes this shift in direction.

Why are Goggles Used While Swimming?

The focal length of the eye alters upon contact with water. The goggles have a focal length that enhances the swimmer's vision. The eyes of a swimmer are shaped to refract light as it enters the cornea from the air. This is upheld by the goggles. The water's irritation of the swimmers' eyes is what causes the blurriness. Swimmers' eyes are protected with goggles.

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The distance to the epicenter by using the equation D = ΔT 8.4 is 16.8 kilometers.

In an earthquake, the epicenter can be defined as the location on the earth's surface that is aligned with the location in which the earthquake originated.

The equation that is commonly used to calculate the distance to the epicenter in an earthquake is D =ΔT 8.4. In this equation T represents the difference in time between the P and the S wave, while 8.4 represents a constant.

Based on this, let's calculate the distance:

D =ΔT 8.4

D = 2 x 8.4

D = 16.8 km

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Answer:

10. If two objects are moving but the total momentum of the system is zero, the momentum of the two objects are equal in magnitude but opposite in direction.

11.

a. The momentum of the system before they push off each other is zero as they both start at rest.

b. The total momentum of the system after they push off each other must be zero, as the law of conservation of momentum states that the total momentum of a closed system remains constant.

c. If the girl skater has a mass of 30 kg and moves backward at 5 m/s, the velocity of the boy skater would be in the opposite direction at 5 m/s. This can be found using the equation p = mv, where p is momentum, m is mass, and v is velocity. Since the total momentum of the system is zero, the momentum of the girl skater (30 kg * -5 m/s) must be equal in magnitude but opposite in direction to the momentum of the boy skater (50 kg * v). So, v = (30 kg * -5 m/s) / 50 kg = -5/50 m/s = -0.1 m/s.

d. The force exerted on each skater can be found using the equation F = Δp/Δt, where F is force, Δp is the change in momentum, and Δt is the time over which the force is exerted. Using the known values, F = Δp/Δt = (0 - 0) / 2.5 s = 0 N. This means that the force exerted on each skater is zero.

The formula y = - 1 2 g t 2 y = - frac 1 2 g t 2 y=-21gt2 describes the vertical distance from the ground, where g is the acceleration of gravity and h is a height.

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Let's assume the speed of the boat relative to the water is s.

The time taken for the boat to travel 1.42 km upstream is t1.

The time taken for the boat to travel 1.42 km downstream is t2.

The velocity of the river is v.

Since the speed of the boat relative to the water is constant, we have:

Upstream:

v + s = s + (1.42 km) / t1 = (1.42 km) / t1 km/hr

Downstream:

v - s = (1.42 km) / t2 km/hr

Since the boat takes 75 min for the round trip, we have:

t1 + t2 = 75 min = 1.25 hours

Rearranging the above equations, we have:

v = (1.42 km / t1 - 1.42 km / t2) / 2 km/hr

Substituting t1 + t2 = 1.25 hours, we have:

v = (1.42 km / (1.25 hours - t2) - 1.42 km / t2) / 2 km/hr

Since t2 = 1.25 hours - t1, we have:

v = (1.42 km / (1.25 hours - (1.25 hours - t1)) - 1.42 km / (1.25 hours - t1)) / 2 km/hr

v = (1.42 km / (1.25 hours) - 1.42 km / (2.5 hours - t1)) / 2 km/hr

Finally, solving for t1, we have:

t1 = (1.42 km / v) * 2 km/hr / (1 + (1.42 km / (1.25 hours * v))) hours

So, the flow velocity of the river is v.

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The acceleration due to gravity is 9.8 m/s2, the tension in the cord is equal to 98 N.

Acceleration is the rate of change of velocity over time. It is a vector quantity, meaning it has both direction and magnitude. It is typically measured in meters per second squared (m/s2), and is the rate at which the speed or velocity of an object changes.

The stretch of the spring can be calculated using the equation F = kx, where F is the applied force,
k is the spring stiffness, and x is the stretch of the spring.
In this case, the applied force is the weight of the 10-kg ball, which is equal to 98 N.
Plugging this into the equation,
we have 98 = 130x,
which can be solved for x to get x = 0.75 cm.

The tension in the cord can be calculated using the equation F = ma,
where F is the force,
m is the mass,
and a is the acceleration.
Since the acceleration due to gravity is 9.8 m/s2, the tension in the cord is equal to 98 N.

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A ball is thrown upwards and returns to the same position. Compared with its original speed after relase, its speed when it returns is about the same.

To solve this case, we will use energy conservation and free fall concepts.

Energy conservation defines that the energy in a system will remains the same as long as no other external force working in the system. Energy in a system will not be created or destroyed, but only change its form from one to another.

We will use the energy conservation concepts in this case under the kinetic and potential energies approach.

When the ball is thrown upwards, the ball has its kinetic energy and zero potential energy. As the ball goes higher, it will reach its highest peak once all of its kinetic energy has change into potential energy. The potential energy then will change into kinetic energy directly as the ball falls into its initial position. We can formulazid these moments as:

E1 = E2 = E3

where:

E1 = total energy when the ball is thrown upwards

E2 = total energy when the ball just stop at its highest peak

E3 = total energy when the ball starts to drop into its initial position

E1 = E2 = E3

Ek1 + Ep1 = Ek2 + Ep2 = Ek3 + Ep3

1/2 mv1² + mgh1 = 1/2mv2² + mgh2 = 1/2mv3² + mgh3

1/2mv1² + mg(0) = 1/2m(0)² +mgh = 1/2mv3² + mg(0)

1/2v1² = gh = 1/2v3²

v1² = v3² =2gh

v1 = v3 = √2gh

The ball will falls with the same speed as the speed when it was thrown upwards.

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The kinetic energy of an object of mass 10kg when it is moving with a velocity 2ms⁻¹ is  20 joule.

The energy an object has as a result of motion is known as kinetic energy in physics. It is described as the effort required to move a mass-determined body from rest to the indicated velocity.

The body holds onto the kinetic energy it acquired during its acceleration until its speed changes.

Mass of the object: M = 10 kg.

Velocity of the object: v = 2 m/s.

Hence, the kinetic energy of the object = 1/2×Mv²

= 1/2 × 10 × 2² joule

= 20 joule.

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