a 135-kg k g astronaut (including space suit) acquires a speed of 2.70 m/s m / s by pushing off with her legs from a 1900-kg k g space capsule. use the reference frame in which the capsule is at rest before the push.
A) What is the velocity of the space capsule after the push in the reference frame? B)If the push lasts 0.660 s , what is the magnitude of the average force exerted by each on the other? C)What is the kinetic energy of the astronaut after the push in the reference frame? D)What is the kinetic energy of the capsule after the push in the reference frame? I am down to only one answer left on A and B and cannot seem to get them correct, so if you could work it out for me that would be the best. Thank you.

The ball is in the air for about 1.8 seconds before it hits the ground after it leaves the student's hand with a speed of 11 m/s when the hand is 1.8 m above the ground.

Projectile motion is a kind of movement experienced by an object or particle (a projectile) that is projected near the Earth's surface and moves along a curved path under the gravity of the Earth. In general, projectile motion refers to a free-body's motion influenced only by gravity. A student throws a ball straight up while standing on the ground. When her hand is 1.8 m above the ground, the ball leaves her hand at a speed of 11 m/s. The time the ball is in the air before it hits the ground is calculated as follows:Using the equation:

∆y = v0yt + 1/2gt² Where ∆y is the displacement (in this case, -1.8 m) of the projectile along the vertical axis, v0y is the initial vertical velocity (in this case, 11 m/s), t is the time of flight, and g is the acceleration due to gravity (9.81 m/s²):-1.8 m = (11 m/s)t + (1/2)(-9.81 m/s²)t².Rearranging the equation, we get:-4.905t² + 11t - 1.8 = 0.

Using the quadratic formula, we get:t = (-11 ± sqrt(11² - 4(-4.905)(-1.8))) / (2(-4.905))= 1.77 s or t = 0.20 s. Since the ball is in the air for approximately 1.77 s before it hits the ground, and the student's hand is 1.8 m above the ground, the ball is in the air for about 1.8 seconds before it hits the ground. Therefore, the correct answer is the option C, 1.8 seconds.

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The vertical and horizontal components of the pendulum's maximum displacement are 0.82 m and zero, respectively. No displacement occurs in the horizontal direction because the x-component is zero.



Mass of bullet, m = 29 g = 0.029 kg
Velocity of bullet, v = 210 m/s
Mass of pendulum, M = 3.2 kg
Length of pendulum, l = 2.9 m

Initial velocity of the bullet before colliding with the pendulum can be calculated as v = u + at ⇒ a = (v-u) / t

Here, u = 0 (initial velocity is zero)
t = time of flight of the bullet = 2.9 / (9.81) = 0.295 s
Hence, a = v / t = 210 / 0.295 = 712.71 m/[tex]s^2[/tex]

The momentum of the bullet just before hitting the pendulum can be given as:
p = m * v = 0.029 * 210 = 6.09 N s

Let us assume that after hitting the pendulum, the bullet and the pendulum stick together and move with a velocity 'V' (as shown in the figure).

Bullet and Pendulum moving together

According to the principle of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision:

(m * v) = (M + m) * V
⇒ V = m * v / (M + m)
⇒ V = 0.029 * 210 / (3.2 + 0.029)
⇒ V = 4.03 m/s

Now, the pendulum moves to a maximum height which can be calculated using the principle of conservation of energy:

Initial KE + Initial PE = Final KE + Final PE
1/2 * (M + m) * [tex]V^2[/tex] + 0 = (M + m) * g * h
⇒ h = [tex]V^2[/tex] / (2*g)
⇒ h = [tex]4.03^2[/tex] / (2*9.81)
⇒ h = 0.82 m

Part A: The vertical component of the pendulum's maximum displacement is 0.82 m.

Part B: The horizontal component of the pendulum's maximum displacement is zero.

The bullet hits the pendulum and gets embedded into it. After the collision, the bullet and the pendulum stick together and move with a common velocity 'V'.The pendulum moves to a maximum height of 0.82 m (which is the maximum displacement in the vertical direction). However, there is no displacement in the horizontal direction (i.e., the x-component of displacement is zero).

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For calculation of potential energy mass of the apple , average acceleration of the apple and height of apple is required.

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1) The force constant of the spring is 0.76N/cm, 2) The magnitude force needed to stretch the spring 5.00cm from its unstretched length is 3.80N, 3) Work done to compress this spring 4.00 cm from its unstretched length is 12.48J, 4) Force needed to stretch it this distance is 3.04N.

1- To calculate the force constant of the spring, you need to use the equation W = 1/2 kx2, where W is the work done to stretch the spring, k is the force constant and x is the stretch distance. In this case, W = 19.0J and x = 5.00cm, so k = 19.0/25 = 0.76N/cm.

2- To calculate the magnitude of the force needed to stretch the spring 5.00cm from its unstretched length, you need to use the equation F = kx, where F is the force, k is the force constant, and x is the stretch distance. In this case, F = 0.76N/cm x 5.00cm = 3.80N.

3- To calculate the work done to compress this spring 4.00 cm from its unstretched length, you need to use the equation W = 1/2 kx2, where W is the work done to compress the spring, k is the force constant and x is the compression distance. In this case, W = 1/2 x 0.76N/cm x (4.00 cm)2 = 12.48J.

4- To calculate the force needed to stretch the spring this distance, you need to use the equation F = kx, where F is the force, k is the force constant, and x is the stretch distance. In this case, F = 0.76N/cm x 4.00cm = 3.04N.

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Using the line's straight segment in figure 10, it is possible to determine the usable power output of the kettle.

The period that the kettle is heating the water up until it reaches boiling point is depicted by the straight segment of the line in figure 10. Both the  power input to the kettle and the rate of energy transfer to the water remain constant throughout this period. Hence, by dividing the energy that was transmitted to the water during this period by the whole amount of time, the usable power output of the kettle can be determined. The straight section's slope, which reflects the rate of energy transfer, and horizontal distance, which indicates the elapsed time, may be used to calculate this. The energy transmitted is calculated by dividing the rate of energy transmission by the amount of time.

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Water is considered a crucial ingredient for the existence of life as we know it.  It is a universal solvent that facilitates biochemical reactions, and its unique properties allow it to maintain a stable temperature range,

making it an ideal medium for the evolution of complex life forms.

One of the key requirements for life to exist is the presence of liquid water. Water is essential for the formation and maintenance of cell structures and for the transport of nutrients and waste products in living organisms. Therefore, when scientists search for extraterrestrial life, they focus on finding evidence of liquid water on other planets or moons.

In our solar system, Mars and several of Jupiter's moons, such as Europa and Ganymede, have been identified as potential locations for the presence of liquid water. Recent discoveries of underground oceans on some of these moons have increased the possibility of finding extraterrestrial life.

Additionally, the search for exoplanets, planets beyond our solar system, has become an important focus of astrobiology research. Astronomers use various techniques to identify exoplanets that may be within the habitable zone of their host star, where temperatures are just right for liquid water to exist.

In summary, water is a critical component for life as we know it, and its presence on other planets or moons greatly increases the chances of finding extraterrestrial life.

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The state of the connection in host A before receiving the ACK from B: Before receiving the ACK from B, the state of the connection in Host A was in the FIN WAIT 1 state.                                                                                                            The state of the connection in host A after receiving the ACK: After receiving the ACK, the state of the connection in Host A is in the FIN WAIT 2 state.

In the 1st phase, the FIN segment is sent by the side which initiates the closing of the connection. The other side responds with an ACK that indicates that the FIN segment was received. The connection will stay in this state until a FIN segment is received by the other side or the timeout timer expires.

In the second phase of the termination process, the side receiving the FIN segment responds with an ACK. If it has any remaining data to send, it can do so in this phase, and the connection stays in FIN WAIT 2 state. If not, it moves to the TIME WAIT state, which is the final step in the termination process.

Therefore, the state of the connection in Host A is in the FIN WAIT 2 state after receiving the ACK.

What is TCP?

TCP is an abbreviation of Transmission Control Protocol. It is the protocol that serves as the foundation of the internet. It works to ensure that data sent over a network is delivered to the correct recipient. It is a connection-oriented protocol that means it needs to establish a connection before transmitting any data.

TCP guarantees that data sent over the internet reaches the intended recipient without data loss, duplication, or corruption.

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It is estimated that the frequency for which the specific solution has the maximum amplitude is 0.971825315808.

The differential equation is as follows: dy/dt + 3y iwt = e(t2)

If we assume that the specific answer is of the form Aeiwt, we may substitute it in the equation to obtain the following result: (iwt + 3).

Aeiwt equals e(t2).

We arrive at A = e(-t2) / (iwt + 3) after solving for A.

The modulus of A, which is |A| = e(-t2) / sqrt(w2 + 9) gives the amplitude of the specific solution.

We must reduce the denominator of |A| with respect to w in order to determine the frequency at which the amplitude is greatest.

After differentiating and setting it to zero, we arrive at w = 0.971825315808 by applying the formula: -9 / 2(w2 + 9)(3/2) = 0.

Hence, for this specific solution, the frequency for which the highest amplitude is present is around 0.971825315808.

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The diameter of the pinhole is 0.1220 mm, through which the sunlight is passing through and making a small patch of light on the far wall.

Given information,

width of central maxima  = 3 cm = 3×10⁻²m

size of the pinhole, a = 3 m

The  average wavelength of sunlight, λ = 500 nm

The small bending of light as it travels around an object's edge is known as diffraction. The ratio of the wavelength of the light to the opening size determines how much bending occurs.

The relation between wavelength and aperture diameter is expressed as,

w = 2.44λa/D

where D is the diameter of the pinhole,

D = 2.44λa/w

D = 2.44×500×10⁻⁹×3/3×10⁻²

D = 0.1220×10⁻³m

D =  0.1220 mm

Hence, the diameter of the pinhole is 0.1220 mm.

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The corresponding electric force on an electron near the surface of the earth is approximately 1.76 x 10^−19 N, while the gravitational force from the earth on the same electron is approximately 9.08 x 10^-30 N. This shows that the gravitational force is much weaker than the electric force.

To shield the electron from this force, one can use a Faraday cage, which is an enclosure made of conductive materials that can block external electric fields.

The cage works by redistributing the charges so that they cancel out the external electric field. In the case of a fluctuating electric field, the cage will continue to protect the electron as long as the field changes are not too rapid. For stronger or rapidly changing fields, other types of shielding may be necessary.

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Unbalanced net forces that are not counterbalanced by opposing forces cause an object's motion to accelerate.

Unbalanced net forces have the following two properties: they alter an object's motion, and they are not counteracted by other forces. When an item is subjected to an imbalanced net force, the object accelerates in the direction of the net force. The amount of Acceleration is inversely proportional to the object's mass and directly proportional to the amount of net force. When the forces exerted on an item are not counterbalanced by opposing forces, an imbalanced net force develops. This indicates that a force has been generated as a result, changing the object's velocity. The comprehension of motion and forces in physics depends on these qualities.

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Answer:

Explanation:

The triboelectric effect (also known as triboelectric charging) is a type of contact electrification on which certain materials become electrically charged after they are separated from a different material with which they were in contact.

The visible light spectrum is the range of wavelengths the human eye can detect, ranging from 380 to 700 nanometers.

People think of the sun, light bulbs, candles, and flames when they think of light, but visible light originates from many sources and in many hues. Other visible light sources include television and computer displays, glow sticks, and pyrotechnics.

This is why this area of the electromagnetic spectrum is known as the visible spectrum or colour spectrum. It primarily comprises of seven colours: violet, blue, green, yellow, orange, and red.

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Answer:

It is the three spots where there are lines. Between 400 and 500(the two lines), between 600 and 700(the two lines), and the one line between 700 and 800.

Answer:B

Explanation:The ray above makes a 90 degree angle. The ray below makes a 60 degree angle.

In the case where the car is traveling in the -x direction and decreasing in speed, it has a negative velocity and a positive acceleration. Therefore, option D is the correct answer. In this case, the car is traveling in the - direction and decreasing in speed. Therefore, it has a negative velocity and a positive acceleration.

Let's discuss the given options one by one:

(A) In this case, the car is traveling in the -x direction at a constant speed. Therefore, it has a negative velocity and zero acceleration. This option is incorrect.

(B) In this case, the car is traveling in the - direction and increasing its speed. Therefore, it has a negative velocity and a positive acceleration. However, the given direction is not specified, and thus this option is not accurate.

(C) In this case, the car is traveling in the +x direction and increasing in speed. Therefore, it has a positive velocity and a positive acceleration. This option is incorrect.

(D) In this case, the car is traveling in the - direction and decreasing in speed. Therefore, it has a negative velocity and a positive acceleration. This option is correct.

(E) In this case, the car is traveling in the +x direction and decreasing in speed. Therefore, it has a positive velocity and a negative acceleration. This option is incorrect.

Therefore, Option D ( - direction decreasing in speed) is correct.

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Answer:

how does the amount of strokes on a magnet affect the strength of it? Note- I'm NOT a high schooler. Simple answers please. I'm 11.

Explanation:

The amount of strokes on a magnet does not affect its strength. The strength of a magnet depends on the properties of the materials it is made of, such as the type of metal and the way it is magnetized. Once a magnet is magnetized, it will retain its strength unless it is exposed to high temperatures or strong magnetic fields that can demagnetize it.

The airplane should head in a direction of 298.93° relative to north in order to arrive at a point due west of its location.

To calculate this, first calculate the speed of the airplane relative to the ground.

The airplane's speed relative to the ground is:
Speed relative to ground = Speed relative to air + Wind Speed
= 275 mi/h + 35 mi/h
= 310 mi/h
Next, calculate the direction relative to north of the airplane's movement. The direction relative to north is calculated using the following formula:
Direction relative to north = tan-1(Opposite/Adjacent)
= tan-1(35 mi/h/310 mi/h)
= tan-1(0.1145)
= 298.93°
Therefore, the airplane should head in a direction of 298.93° relative to north in order to arrive at a point due west of its location.

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The boy coasts down the hill on the sled and reaches a level surface with a speed of 7.2 m/s. The coefficient of friction between the sled's runners and the snow is 0.055, and the boy and sled together weigh 540 N. To determine how far the sled will travel on the level surface before coming to rest, we need to calculate the distance using the formula Distance = (Speed x Time) - (1/2 x Acceleration x Time2). We can determine the time it takes for the sled to come to rest using the equation Speed = (Friction x Normal Force) / Mass. So, Speed = (0.055 x 540N) / 540N = 0.055 m/s. Time = 7.2/0.055 = 130.9 seconds. We can then calculate the distance as Distance = (7.2 x 130.9) - (1/2 x 0.055 x 130.92) = 927.9 m. Therefore, the sled will travel 927.9 m before coming to rest.

The boy and sled weigh 540 N. A boy coasts down a hill on a sled, reaching a level surface at the bottom with a speed of 7.2 m/s. The coefficient of friction between the sled's runners and snow is 0.055. How far does the sled travel on the level surface before coming to rest?

The distance traveled by the sled on the level surface before coming to rest is 72.22 meters.

What is friction?

Friction is a force that opposes motion. It is the friction between the sled's runners and the snow that causes the sled to stop. The formula for frictional force is:f = μN where f is the frictional force, μ is the coefficient of friction, and N is the normal force, which is equal to the weight of the sled and boy since they are on a level surface. The normal force is given by: N = m*g where m is the mass of the sled and boy and g is the acceleration due to gravity, which is equal to 9.81 m/s^2.

How far does the sled travel on the level surface before coming to rest?

The sled will travel a certain distance, d, before it stops. The distance, d, is given by:d = (v^2 - u^2) / 2fwhere v is the final velocity, u is the initial velocity (which is 7.2 m/s), and f is the frictional force. The frictional force is f = μN = μmgSubstituting the given values:d = (7.2∧2 - 0∧2) / (2*0.055*540*9.81)d = 72.22 meters. Therefore, the sled will travel 72.22 meters on the level surface before coming to rest.

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The difference in loudness between the sound made by a blue whale and a human is 120 decibels.

The loudest sound a human can make is measured at about 140 decibels, while the sound a blue whale can make is measured at about 260 decibels. This means that the blue whale can produce a sound that is 1 million times greater in intensity than the loudest sound a human can make. This difference in loudness is equal to 120 decibels.

The difference in loudness between the sound made by a blue whale and a human is 120 decibels. The loudest sound a human can make is measured at about 140 decibels, while the sound a blue whale can make is measured at about 260 decibels. This means that the blue whale can produce a sound that is 1 million times greater in intensity than the loudest sound a human can make.

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The Kuiper belt is a disk-like region between the outer planets and the Oort cloud. Thus, option A is correct

The Kuiper belt, also known as the trans-Neptunian region, is a doughnut-shaped region of space beyond Neptune that is home to an estimated 100,000 tiny, icy objects.

It is named after Dutch-American astronomer Gerard Kuiper, who first proposed its existence in 1951.

The belt ranges in distance from 30 to 50 astronomical units (AU) from the Sun, which is about 2.8 to 4.7 billion miles away.

The Kuiper belt objects are believed to be remnants from the formation of the solar system. They are small and mostly made up of ice and dust, similar to comets.

Some Kuiper belt objects, such as Pluto and Eris, are classified as dwarf planets.

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Answer:

They were deposited horizontally and then shifted by a geologic event.

Explanation:

The flux through any closed surface surrounding a cylinder with height H and radius R having surface charge density σ = k sin φ, where k is a constant, is φ₀=2πRLk sin φ/ε₀.

Since the cylinder's surface charge density is given by σ = k sin φ

Therefore, the total charge on the cylinder's curved surface

Q = σ(2πRL)

Where L is the height of the cylinder, Q = 2πRLk sin φ .

From Gauss's Law, the total flux through a closed surface surrounding a cylinder with height H and radius R is given by φ₀=Qε₀ .Here, ε₀ represents the vacuum permittivity. Now, substituting the value of Q, we get

φ₀ = (2πRLk sin φ)/ε₀

Therefore, the flux through any closed surface surrounding a cylinder with height H and radius R having surface charge density σ = k sin φ, where k is a constant, is φ₀=2πRLk sin φ/ε₀.

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The correct statement about the relationship between the two forms of Newton's second law (Fnet = dp/dt and Fnet = m.a) is option D "Fnet = m.a reduces to Fnet = dp/dt if the momentum of the object does not change with time.

Newton's second law of motion states that the acceleration of an object is directly proportional to the force applied to it and inversely proportional to its mass. In other words, Fnet = m.a, where Fnet is the net force acting on an object, m is its mass, and a is its acceleration. This law can also be written as Fnet = dp/dt, where dp/dt is the rate of change of momentum with time.

Since momentum is the product of mass and velocity, it can be rewritten as dp/dt = m.dv/dt + v.dm/dt, where v is the velocity of the object. If the mass of the object remains constant over time, then v.dm/dt is zero and dp/dt reduces to m.dv/dt, which is equal to Fnet.

Therefore, Fnet = dp/dt reduces to Fnet = m.a if the object's acceleration does not change with time. If the momentum of the object does not change with time, then dp/dt is zero, and Fnet = dp/dt reduces to zero, which means that Fnet = m.a is also zero. Therefore, Fnet = m.a reduces to Fnet = dp/dt if the momentum of the object does not change with time.

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plq1. If the glider is more massive than expected, or the force applied to the glider is less than expected, the acceleration data is affected because the acceleration of the object is inversely proportional to the mass of the object. plq2. If the force applied to the glider is greater than expected, or the glider is less massive than expected, the acceleration data is affected because the acceleration of the object is directly proportional to the force applied to it

The acceleration of the object can be calculated using the following formula: F=maWhere F is the force applied to the object, m is the mass of the object, and a is the acceleration of the object. If the mass of the object is more than expected, the acceleration of the object decreases, resulting in a lower acceleration reading. Similarly, if the force applied to the object is less than expected, the acceleration of the object decreases, resulting in a lower acceleration reading.

If the force applied to the object is greater than expected, the acceleration of the object increases, resulting in a higher acceleration reading. Similarly, if the mass of the object is less than expected, the acceleration of the object increases, resulting in a higher acceleration reading.

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The correct statements are as follows: Option (b), (c) and (d). A modified Warren Truss is a variant of the standard Warren truss, which is characterized by having verticals in every other panel.

A Warren truss is a type of truss having similar lengths for all of its members, and where the members are connected via a series of equilateral triangles that are arranged alternatively pointing upwards and downwards.

The vertical webs are useful for bracing the top chord against buckling upward and downward. The vertical webs support parts of the top chord, thereby reducing the span, and associated bending stress, of the top chord under the uniform gravity force of the decking resting on the top chord of the truss. Therefore the correct answers are options (a), (b), and (d).

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The potential difference across a capacitor after it has been discharging for a very long time is 0 volts. This is because the capacitor is empty of charge, and thus has no potential difference between its two terminals.

A capacitor is a type of electrical component that stores energy in an electric field. The energy is stored in the form of electric charges on two conductive plates.

The plates are separated by an insulating material called a dielectric. The potential difference across a capacitor is proportional to the amount of charge stored on the plates.

When a capacitor discharges, it loses the stored charge. This discharge occurs when the capacitor is connected to a circuit. The capacitor will then begin to discharge as the charges on the plates flow through the circuit.

The potential difference across the capacitor will decrease as the charges on the plates decrease.

The capacitor has been completely discharged and no longer has any potential difference.

Thus, the potential difference across a capacitor after it has been discharging for a very long time is zero.

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We always see the same side of the Moon because the "Moon rotates on its axis once for each revolution around Earth." Thus, the correct option will be B.

When the Moon rotates on its axis once for each revolution around Earth, then we always see the same side of the Moon. The reason behind this is that the moon's rotation takes almost the same time as it takes to orbit the Earth.

When the same side of the moon is facing the Earth, it appears to be unchanging. That is why we always see the same side of the moon from Earth. The other side of the Moon is known as the far side, which was first observed by the Soviet spacecraft Luna 3 in 1959.

Therefore, the correct option will be B.

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To produce a 24.0 V peak emf, the field strength needed for a car generator with a 300-turn, 5.05 by 8.2 cm rectangular coil rotating at 400 rpm when the engine is idling is 1.6 V/m.

Аn electromotive force (EMF), often known аs voltаge, is аn electricаl force thаt drives current through аn electricаl circuit. EMF is а meаsure of the energy per unit chаrge thаt аn electricаl power source, such аs а bаttery or generаtor, gives to electrons trаveling through а circuit. The symbol for EMF is E.

The mаgnetic field strength cаn be determined using the formulа:

= BΦ / А×N

where B represents the field strength, Φ represents the flux, А represents the аreа of the loop, аnd N represents the number of turns. To obtаin the field strength, first, compute the flux, then use the formulа given аbove for B.

This is mathematically expressed as:

B = E / (NAB)

Here,

E = 24.0 V

N = 300 turns

A = 5.05 cm × 8.2 cm = 41.41 cm²

= 0.004141 m

2BΦ / A × N = E/ NAB

⇒ Φ / A = E/ BN2A2BΦ = EN2ABΦ

= (24.0V)×2(300)(0.004141 m²)Φ

= 7.26 x [tex]10^{-4}[/tex] Wb

B = Φ / ANB = Φ / ANB = 7.26 x [tex]10^{-4}[/tex] Wb / 300(0.004141 m²)

B = 0.0762 T

Therefore, to produce a 24.0 V peak emf, the field strength required is 0.0762 T.

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If an electron at the surface of the negative plate were released from rest, its velocity would depend on the potential difference between the plates.

Potential difference (V) is the work done per unit charge. Its unit is volts (V). When a potential difference is applied between the two plates of a capacitor, the potential difference is given by the equation V = Q/C, where Q is the charge on the plates and C is the capacitance of the plates.If an electron is released from rest at the surface of the negative plate, it will move towards the positive plate. The potential difference between the two plates will create an electric field that will cause the electron to accelerate.

The acceleration of the electron is given by the equation a = F/m, where F is the force on the electron and m is its mass. The force on the electron is given by F = Eq, where E is the electric field strength and q is the charge on the electron. Therefore, the acceleration of the electron is given by a = Eq/m.After a time t, the velocity of the electron is given by v = at. Therefore, the velocity of the electron at any time t is given byv = (Eq/m)t.Note: It is important to note that this equation is only valid for small potential differences. If the potential difference is large enough, the electron may acquire relativistic velocities, and the equation will no longer hold.

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Answer:

Approximately [tex]705\; {\rm m}[/tex].

Explanation:

Let [tex]x[/tex] denote the distance travelled before the plane takes off.

Let [tex]u[/tex] denote the initial velocity of the plane, and let [tex]v[/tex] denote the velocity of the plane when it takes off. It is given that the takeoff speed is [tex]v = 65\; {\rm m\cdot s^{-1}}[/tex]. Assuming that the plane was initially stationary, initial velocity would be [tex]u = 0\; {\rm m\cdot s^{-1}}[/tex].

It is given that the acceleration of the plane would be [tex]a = 3\; {\rm m\cdot s^{-2}}[/tex].

Since acceleration is constant, apply the SUVAT equation [tex]x = (v^{2} - u^{2}) / (2\, a)[/tex] to find the value of [tex]x[/tex]:

[tex]\begin{aligned} x &= \frac{v^{2} - u^{2}}{2\, a} \\ &= \frac{(65)^{2} - (0)^{2}}{2\, (3)}\; {\rm m} \\ &\approx 705\; {\rm m}\end{aligned}[/tex].

(Rounded up.)

Hence, the length of the runway should be at least [tex]705\; {\rm m}[/tex].