sally is an astronaut who has a mass of 60 kg. currently she is conducting experiments in a permanent space station that is orbiting earth at an altitude equal to earth's radius. refer to exhibit 5-1. what is the force of gravity acting on sally while she is in the space station?

A softer landing occurs when a falling object bounces from a surface. This is a common occurrence when an object with some degree of elasticity is dropped.

When it strikes a surface, the object's kinetic energy is transformed into potential energy. When it bounces back, some of that potential energy is transformed back into kinetic energy, resulting in a bounceback.A softer landing occurs when a falling object bounces from a surface due to elasticity.

For instance, when a ball is dropped, it hits the ground, and a softer landing occurs when the ball bounces from the ground, causing it to absorb less impact than if it had just hit the ground. Soft landings can happen when a surface is made of a soft or elastic material that can deform and absorb some of the impact, reducing the force of the landing.A ball with more elasticity will bounce higher than a ball with less elasticity.

This is due to the fact that a ball with higher elasticity will rebound with more kinetic energy, resulting in a higher bounce. A softer landing can also occur if the surface that the object lands on is cushioned or padded, such as when a person jumps onto a foam mat.

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The velocity vector is r'(t) = (4, -3 sin t, 3 cos t), the acceleration vector is r''(t) = (0, -3 cos t, -3 sin t), the curvature is κ = 3 / 14^(3/2), and the tangential and normal components of the acceleration are aT = 0 and aN = 3.

Space Curves: Arc lengthArc length formula is given by \(L = ∫a b |r'(t)|dt\)

, where r(t) is the vector function for the given curve.

Let's find the arc length of the given space curve:

r(t) = (2t, t^2 - 2, 5 - t^2) for 0 ≤ t ≤ 4.

The speed of r(t) is |r'(t)|.r'(t) = (2, 2t, -2t) and

||r'(t)|| = √(2^2 + (2t)^2 + (-2t)^2)

= 2√2t.So,

the arc length of the space curve is

L = ∫0 4 2√2t dt

= (4/3)√2 [t^(3/2)] from 0 to 4

= (4/3)√2 (4√2 - 0)= (16/3) * 2

= 32/3.

Therefore, the length of the given space curve with vector equation is 32/3. Vector Functions for the intersection of two surfaces

The equation for the given surface is \(F(x)=(2,x²-30).\)

Let's find the vector functions for the intersection of two surfaces.

To find the intersection, we equate the two given equations:2 = y = x².

We get y = x² = 2. So, x = ±√2.

The vector functions for the intersection of two surfaces are:

r1(t) = (t, 2, t^2 - 30)

for x = √2 and r2(t)

= (-t, 2, t^2 - 30)

for x = -√2.

Given TNB for a space curveLet's find the unit tangent vector to the space curve r(t) = (cos t, sin t, t).

The velocity vector is r'(t) = (-sin t, cos t, 1).

The speed of the curve is |r'(t)| = √(sin² t + cos² t + 1) = √2.

The unit tangent vector is T = r'(t) / |r'(t)| = (-sin t/√2, cos t/√2, 1/√2).

Now, let's find a unit normal vector to the space curve.The acceleration vector is r''(t) = (-cos t, -sin t, 0).

The magnitude of acceleration is |r''(t)| = 1.

The unit normal vector is N = r''(t) / |r''(t)| = (-cos t, -sin t, 0).The binormal vector is given by B = T × N.

Therefore, the unit tangent vector to the space curve r(t) = (cos t, sin t, t) is T = (-sin t/√2, cos t/√2, 1/√2),

the unit normal vector is N = (-cos t, -sin t, 0),

and the unit binormal vector is

B = (cos t/√2, -sin t/√2, 1/√2) × (-cos t, -sin t, 0)

= (sin t/√2, -cos t/√2, 1/√2).

Velocity, acceleration and curvature

Let's find the velocity vector, the acceleration vector, and the curvature of the space curve r(t) = (4t, 3 cos t, 3 sin t) for 0 ≤ t ≤ 27.

The velocity vector is r'(t) = (4, -3 sin t, 3 cos t).

The speed of the curve is |r'(t)| = √(16 + 9 sin² t + 9 cos² t) = 5.

The unit tangent vector is T = r'(t) / |r'(t)| = (4/5, -3 sin t/5, 3 cos t/5).

The acceleration vector is r''(t) = (0, -3 cos t, -3 sin t).

The magnitude of acceleration is |r''(t)| = 3.

The tangential component of acceleration is aT = T · r''(t) = 0.

The normal component of acceleration is aN = |r''(t)| · |N| = 3.

The unit normal vector is N = (-cos t, -sin t, 0).

The curvature is κ = |r''(t)| / |r'(t)|² = 3 / (25 + 9 sin² t + 9 cos² t)^(3/2) = 3 / (25 + 9)^(3/2) = 3 / 14^(3/2).

Therefore, the velocity vector is r'(t) = (4, -3 sin t, 3 cos t),

the acceleration vector is r''(t) = (0, -3 cos t, -3 sin t),

the curvature is κ = 3 / 14^(3/2), and the tangential and normal components of the acceleration are aT = 0 and aN = 3.

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Answer:

2.5 m/s²

Explanation:

Given,

Initial speed ( u ) = 10 m/s

Final speed ( v ) = 20 m/s

Time ( t ) = 4 seconds

To find : Acceleration ( a ) = ?

Formula : -

a = ( v - u ) / t

a = ( 20 - 10 ) / 4

= 10 / 4

= 5 / 2

a = 2.5 m/s²

Therefore,

The acceleration of the scooter is 2.5 m/s²

The magnitude e of the electric field be if the charge is to hit the target on the screen is E = mv₀²yh/0.5qL².

Charge's speed in the x direction is equal to v₀.

The charge's time to reach the screen at a distance L, t = L/v₀

F = qE = ma, which is the force on the charge

When the two equations are equalized, force ma = qE/m and charge a = qE/m

The charge's initial velocity in the y-direction is o, and the vertical distance it covers is given by the equations

y = 0.5 (qE/m) (L/v₀)

y = 0.5qL²E/mv² and y = 0.5at².

If the target on the screen is the charge's intended target, y = yh

yh = 0.5qL²E/mv²

Making E the formula's subject, the following is the size of the electric field:

E = mv₀²yh/0.5qL².

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The magnitude of the magnetic force acting on the charge which moves to the right is 0 N.

Given to us,

the charge \(q\) =  \(5\times 10^{-7}\) C,

the velocity \(v\) = \(2.6\times 10^5\)  m/sec,

the magnetic field \(B\) = \(10^{-2}\) T,

angle between the direction of v and B \(\theta\) = 0,

Magnetic force is as important as the electrostatic or Coulomb force. The magnitude of the magnetic force F on a charge q moving at a velocity of v in a magnetic field of strength B is given by

\(\begin{aligned}F&=qvB\ sin\Theta\\&= 5\times10^{-7}\times2.6\times10^5\times10^{-2} \times sin(0)\\&= 0\ N\\\end{aligned}\)

Hence, the magnitude of the magnetic force acting on the charge which moves to the right is 0 N

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When classifying the 36 cells into their individual phases of mitosis ,Inter phase had the highest representation of cells .So option B is correct.

Pro phase is the first phase of mitosis, and it is when the chromosomes condense and become visible. The nuclear envelope breaks down, and the spindle fibers form.

Meta phase is the second phase of mitosis, and it is when the chromosomes line up along the spindle fibers. The chromosomes are then pulled apart by the spindle fibers.

Ana phase is the third phase of mitosis, and it is when the chromosomes are pulled to opposite poles of the cell. The cell then begins to divide.

Telophase is the final phase of mitosis, and it is when the cell divides into two daughter cells. The chromosomes uncoil, and the nuclear envelope reforms.Therefore option B is correct.

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Electric potential is the amount of electric potential energy per unit charge at a particular point in an electric field.

It is a scalar quantity measured in volts (V). To find the value of charge (q) given the electric potential, we can use the equation:

Electric Potential = Electric Potential Energy / Charge

Rearranging the equation, we have:

Electric Potential Energy = Electric Potential * Charge

The electric potential energy is the work done to bring a charge from infinity to a specific point in the electric field. By knowing the electric potential and rearranging the equation, we can determine the value of the charge (q).

For example, if the electric potential is 10 volts and the electric potential energy is 50 joules, we can substitute these values into the equation:

50 joules = 10 volts * Charge

By rearranging the equation and solving for Charge, we find that the value of the charge (q) is 5 coulombs.

It is important to note that the electric potential is a property of the electric field, while the charge is a property of the particle experiencing the electric field.

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(a) By equation of motion, the velocity of the can just before it hits the water is 22.563 m/s.

(b) The height of the bridge is 25.95 meters.

Accidentally, a painter drops a paint can from a bridge over a river.

For a time t = 2.3 seconds the acceleration is 9.81 m/s².

Initially, the paint can was on rest.

So, the initial velocity is u = 0 m/s.

Using the equation of motion,

v = u + at

Substituting the values,

v = 0 + 9.81 × 2.3

v = 22.563 m/s

(b) Using the second equation of motion,

The height of the bridge is:

s = ut + ( 1/2 )at²

s = 0 × 2.3 + ( 1/2 ) × 9.81 × ( 2.3 )²

s = ( 1/2 ) × 9.81 × 2.3 × 2.3

s = 51.8949 / 2

s = 25.95 m

The final velocity of the can is 22.56 m/s and the height of the bridge is 25.95 meters.

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Explanation:

so I think it B hope that I helped you can good lick

Answer:

ok so first ur not a failure and its okay don't be so hard on ur self

(a) The efficiency of the PV panel can be calculated using the formula:Efficiency = (Power output / Power input) × 100Where,Power output = The power generated by the PV panel (300 W in this case)Power input = The solar insolation (1000 W/m2 in this case) × Area of the panel (2.0 m2 in this case)Efficiency = (300 / (1000 × 2)) × 100= 15%

(b) The total power generated by 10 pieces of 300 W PV panels is given as:Total power = Power of 1 panel × Number of panels= 300 × 10= 3000 WPeak sun hours in Wyoming = 3.2 hours Therefore, the total energy produced daily is given as:Energy produced = Total power × Peak sun hours= 3000 × 3.2= 9600 Wh or 9.6 kWh(c) The energy produced by the PV panel is given as:Energy produced = Power output × Time= 300 × 3.2 × 50/100= 48 kWh= 48,000 Wh= 48,000 / 3.6 × 106 kWh= 0.013 kWh or 13 Wh Weight of 1 gallon of water = 4.546 × 1 = 4.546 kg Mass of water = Volume × Density= 4.546 × 15 = 68.19 kg= 68.19 / 1 = 68.19 liters

Heat required to increase the temperature of 1 liter of water from 15°C to 55°C is given as:Heat = mass × specific heat capacity × temperature rise= 1 × 4.18 × (55 - 15)= 209.2 JHeat required to increase the temperature of 68.19 liters of water from 15°C to 55°C is given as:Heat = 68.19 × 209.2 J= 14,250 J or 0.01425 kWh Energy produced by the PV panel is 0.013 kWh Therefore, the number of gallons of water that can be heated up is given as:Number of gallons = Energy produced / Heat required= 0.013 / 0.01425= 0.91 gallons Therefore, the PV panel can supply to heat up 0.91 gallons of water from 15°C to 55°C.

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Answer:

Designing experiments to replicate the conditions in which life may have first evolved on Earth

Explanation:

In 1953, Stanley L. Miller and Harold C. Urey conducted an experiment to prove that life started from inanimate objects. The research was conducted by utilizing proposed chemical substances, mixed together through a scientific design process. The outcome of the research is the predicted atmospheric conditions before the pre-living form started on earth.

Therefore, in this case, the action that might lead scientists to develop new explanations about the universe is "Designing experiments to replicate the conditions in which life may have first evolved on Earth."

Answer:

The maximum pressure is 10 V from across condenser.The highest charge mostly on condenser. 
Vc  = 10 x 1mf

= 10 ^ - 5C

The time it takes for the condenser to be 5 V different.        
Thus we have, 0.69 x 10 ^ - 3 seconds.

The final speeds of the spheres are 3.47 m/s and 3.08 m/s.

We can use conservation of momentum to solve this problem since there are no external forces acting on the system.

The initial momentum of the system is:

p_initial = m₁ * v₁ + m₂ * v₂

where m₁ and m₂ are the masses of the spheres, and v₁ and v₂ are their initial velocities (4.00 m/s and 0 m/s, respectively).

After the collision, the momentum of the system is:

p_final = m₁ * v1' + m₂ * v₂'

where v₁' and v₂' are the final velocities of the spheres. We also know that the angle between the first sphere's final path and its initial path is 60 degrees, which means that the angle between the two spheres after the collision is 150 degrees (90 + 60).

Using conservation of momentum, we can set the initial and final momenta equal to each other:

m₁ * v₁ + m₂ * v₂ = m₁ * v₁' + m₂ * v₂'

We can also break down the final velocities into their x and y components using trigonometry. Let's define the angle between the first sphere's final path and the x-axis as theta. Now we can use conservation of momentum to solve for the final velocities:

m₁ * v₁ + m₂ * v₂ = m₁ * v₁' * cos(theta) + m₂ * v₂' * cos(150 degrees)

0 = m₁ * v₁' * sin(theta) + m₂ * v₂' * sin(150 degrees)

Solving the first equation for v₂', we get:

v₂' = (m₁ * v₁ + m₂ * v₂ - m₁ * v₁' * cos(theta)) / (m₂ * cos(150 degrees))

Substituting this expression into the second equation and solving for v₁', we get:

v₁' = (m₂ * sin(150 degrees) * v₁ + m₂ * sin(150 degrees) * v₂ + m₁ * sin(theta) * v₁' - m₁ * sin(theta) * m₂ * v₁ * cos(theta) / cos(150 degrees)) / (m₁ * sin(theta))

Plugging in the given values and solving, we get:

v₁' = 3.47 m/s

v₂' = 3.08 m/s

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Thermo-Electrochemical converter (UTEC) is a thermodynamic cycle that does not account for the Carnot Efficiency.

What is the Carnot cycle in thermodynamics?

An ideal closed thermodynamic cycle that is reversible and consists of the four steps of isothermal expansion to a desired point, adiabatic expansion to a desired point, isothermal compression, and adiabatic compression back to the starting state.

What is the purpose of Carnot cycle?

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Answer:

= 1440 kg·m/s

Explanation:

Step by Step Solution to find Momentum of Mass = 288 kg & Velocity = 5 m/s:

Given that,

mass (m) = 288 kg

velocity (v) = 5 m/s

Substitute the value into the formula

p = 288 x 5

p = 1440 kg·m/s

∴ Momentum (p) =1440 kg·m/s

Answer:

400

Explanation:

We divide time (4.5 hours) and speed (1800 miles)

1800÷45=400

The primary distinction between infrared and ultraviolet radiation is that while the wavelength of ultraviolet radiation is shorter than that of visible light, that of infrared radiation is longer.

The part of the electromagnetic spectrum known as ultraviolet radiation spans from the violet, or short-wavelength, end of the visible light spectrum to the X-ray region. High-temperature surfaces, like the Sun's, emit ultraviolet radiation in a continuous spectrum, whereas atomic excitation in a gaseous discharge tube emits it as a discrete spectrum of wavelengths. Both a sterilization method and a research tool, ultraviolet light has several applications. It can also be utilized in fluorescent lights, which use less energy than incandescent bulbs to provide artificial light.

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There are 161  grams of calcium in a sample of calcium-containing 2.42 × 10²⁴ atoms of calcium.

To find the mass of calcium in the sample, we'll use the following steps:

The atomic mass of calcium is 40.078 g/mol. Using Avogadro's number (6.022 × 10²³), we can convert the number of atoms to moles:
2.42 × 10²⁴ atoms / 6.022 × 10²³ atoms/mol = 4.02 mol

Then, we can use the molar mass of calcium to convert moles to grams:
4.02 mol * 40.078 g/mol = 161. 11356 g

Therefore, there are 161.11356  grams of calcium in the sample. Expressing this with three significant figures gives us the final answer of 161 g.

The complete question could be as follows:

A sample of calcium contains 2.42 × 10²⁴ atoms of calcium. How many grams of calcium are there in the sample? Express with three significant figures.

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Answer:

The pressure at the bottom of the river is less than that at the bottom of the lake.

Explanation:

From Bernoulli's equation, the pressure difference is given by

ΔP = ρgΔh + ρ(v₂² - v₁²)/2 where ρ = density of water, g = acceleration due to gravity, Δh = depth, v₁ = velocity at top, v₂ = velocity at bottom

For the lake, v₁ = v₂, since the velocity at the top and bottom are the same. So,

ΔP₁ = ρgΔh + ρ(v₁² - v₁²)/2 = ρgΔh + 0 = ρgΔh

P₂ - P₁ = ρgΔh

P₂ = P₁ + ρgΔh

For the river, v₁ < v₂, since the velocity at the top of the river is greater than at the bottom.

So,

ΔP₂ = ρgΔh + ρ(v₂² - v₁²)/2.

Since  v₁ < v₂, ρ(v₂² - v₁²)/2 will be negative,

So,

ΔP₂ = ρgΔh - ρ(v₂² - v₁²)/2.

Since ρ(v₂² - v₁²)/2 is negative, making ΔP less than that in the lake.

So, ΔP₂ = ΔP₁ -  ρ(v₂² - v₁²)/2.

ΔP₂ = P₃ - P₁

P₃ - P₁ = P₂ - P₁ -  ρ(v₂² - v₁²)/2.

P₃ = P₂ - ρ(v₂² - v₁²)/2.

where P₃ = pressure at bottom of the river and P₂ = pressure at bottom of the lake and P₁ = atmospheric pressure at top of river and lake respectively.

Since the factor ρ(v₂² - v₁²)/2 is removed from the pressure at the bottom of the lake, the pressure at the bottom of the river is therefore less than that at the bottom of the lake.

The drift velocity (v) of charge carriers in a conductor is given by the following equation: v = I / (n \(\times\) A \(\times\) q).

v = I / (n \(\times\) A \(\times\) q)

where:

v is the drift velocity, measured in meters per second (m/s)

I is the current flowing through the conductor, measured in amperes (A)

n is the number of charge carriers per unit volume of the conductor, measured in per cubic meter (\(m^(-3)\))

A is the cross-sectional area of the conductor, measured in square meters (m^2)

q is the charge of a single carrier, such as an electron, measured in coulombs (C)

This equation relates the drift velocity of the charge carriers to the current flowing through the conductor, the number of charge carriers per unit volume, the cross-sectional area of the conductor, and the charge of a single carrier. The drift velocity represents the average velocity of the charge carriers as they move through the conductor in response to an applied electric field.

The number of charge carriers per unit volume (n) depends on the material of the conductor and the temperature. In metals, the charge carriers are typically electrons, and the number density is on the order of 10^28 to 10^29 electrons per cubic meter.

The cross-sectional area (A) of the conductor is the area of the cross-section of the conductor perpendicular to the direction of the current flow, and is a measure of the amount of material available for the charge carriers to move through.

The charge of a single carrier (q) is typically the charge of an electron, which is approximately 1.6 x \(10^{-19\) coulombs.

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Answer:

f = 5000 N

Explanation:

Given that,

The weight of a car = 11000 N

Driving force on the car = 5000 N

We need to find the force opposing the motion of the car. The net force on th car is given by :

F-f = ma

As it moves with constant velocity, a = 0

i.e.

F - f = 0

F = f

f = 5000 N

Hence, the opposing force is 5000 N.

A car starts from rest and undergoes an acceleration of 7.2 m/s² for a duration of 4.5 seconds. The objective is to determine the velocity of the car at the end of this time.

Velocity of the car at the end of the given time, we can use the equation of motion that relates initial velocity, acceleration, and time:

final velocity = initial velocity + (acceleration × time)

Since the car starts from rest (initial velocity = 0), the equation simplifies to:

final velocity = acceleration × time

Plugging in the given values, we have:

final velocity = 7.2 m/s² × 4.5 s

Calculating the expression, we find:

final velocity = 32.4 m/s

Therefore, the velocity of the car at the end of 4.5 seconds, after accelerating at a rate of 7.2 m/s², is 32.4 m/s.

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The kinetic energy of the two-block system before the collision will be \(\frac{9}{2} MV_S^2\). Momentum get conserved during the collision.

The abrupt, violent coming together in direct contact of two bodies is known as the collision.a falling object and a floor are examples of collision.

According to the law of conservation of momentum, the momentum of the body before the collision is always equal to the momentum of the body after the collision.

According to the law of conservation of momentum;

Momentum before collision =Momentum after collision

\(\rm MV+2m(0)=(3M)V_S\\\\ V= \frac{3MV_S}{M} \\\\ V= 3V_S\)

Velocity of the block before collision is \(\rm 3V_S\).

The kinetic energy of the two-block system before the collision is found as;

\(\rm KE = \frac{1}{2} mv^2 \\\\\ \rm KE = \frac{1}{2} m(3V_S)^2 \\\\\ \rm KE = \frac{9}{2} MV_S^2\)

Hence, the kinetic energy of the two-block system before the collision will be \(\frac{9}{2} MV_S^2\).

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A collision is any situation in which two or more bodies quickly exert forces on one another.

Thus, The momentum of the body prior to the contact is always equal to the momentum of the body following the impact, according to the law of conservation of momentum.

The difference between the system's total kinetic energy before and after a collision can be used to categorize collisions in physics:

The collision is said to as being inelastic if the majority or all of the total kinetic energy is lost (dissipated as heat, sound, etc. or absorbed by the objects themselves); such collisions involve the objects coming to a complete stop.

Thus, A collision is any situation in which two or more bodies quickly exert forces on one another.

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Answer:

144 kg m^2/s

Explanation:

The dimensions of the lightest open-top right circular cylindrical can be  6.82cm.

The following is the formula to get the volume of something like a hollow cylinder: The volume of a hollow cylinder is equal to (R2 - r2) h cubic units, where "R" denotes the cylinder's outer radius, "r" its inner radius, and "h" its height. Similar to a prism but having circular bases, a cylinder is a 3-D shape.

Given, volume of the cylinder = 1000cm³

volume of cylinder = πr²h

The bottom and sides are included in the surface area:

SA = πr²+2πrh

The second equation may be written as, after solving the first equation for h.

 SA = πr² +2πr(V/(πr²)) = πr² +2V/r

Where the derivative is 0, the smallest area for the volume will be discovered.

 d(SA)/dr = 2πr -2V/r² = 0

The can radius is thus,

r = ∛(V/π)

and it's height, h = V/(π(V/π)^(2/3)) = ∛(V/π) = r

The dimensions for the specified volume are

r = h = ∛(1000/π) ≈ 6.82cm

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The magnitude of the impulse required to increase its speed from 0. 993c to 0. 996c is  1.53 × 10⁻²¹ kgms⁻¹.

In the atomic nucleus of most atoms, a proton is a subatomic particle that is frequently present. It contains a positive electric charge and is one of the basic building blocks of matter. A proton is an elementary particle with a charge of +1, which is equivalent to the charge of an electron in magnitude but the opposite in sign.

Given values:

Mass, m = 1.7 × 10⁻²⁷ kg

Initial speed, u = 0.993c

Final speed, v = 0.996c

The impulse required to increase the speed of the proton is:
I = mv - mu

I = m(v-u)

I = 1.7 × 10⁻²⁷(0.996 - 0.993)c

I = 1.7 × 10⁻²⁷(0.996 - 0.993) 3 × 10⁸

I = 1.53 × 10⁻²¹ kgms⁻¹

Hence, the magnitude of the impulse required to increase its speed from 0. 993c to 0. 996c is  1.53 × 10⁻²¹ kgms⁻¹.

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Answer:

uv light damages the skin over a long period of time

Explanation:

Some sunlight can be good as long as you have proper protection from overexposure. But too much ultraviolet, or UV, exposure can cause sunburn. The UV rays penetrate outer skin layers and hit the deeper layers of the skin, where they can damage or kill skin

Answer:UV radiation damages DNA in your skin cells, which can accumulate over time and increase the risk of genetic mutations that cause skin cancer. The more often you get burnt, the more damage is done and the higher the risk of skin cancer.

Explanation:

Explanation:

a) The displacement is the area under the curve.

Δx = ½ (10 s) (20 m/s) + (20 s) (20 m/s) + ½ (10 s) (20 m/s)

Δx = 600 m

b) The car is accelerating when the velocity is changing.  This happens between t = 0 and t = 10, and between t = 30 and t = 40.

c) Average speed = displacement / time

v_avg = 600 m / 40 s

v_avg = 15 m/s