A Ford F150 can slow to a stop from 60 m/s in 2.44 seconds with an acceleration of -0.207 m/s2. What is the braking distance of the car?

Answer:

[tex]62.5[\frac{km}{h}][/tex]

Explanation:

if the required speed is 's', then it is possible to make up the next equation:

[tex]\frac{100}{8} =\frac{s}{5};[/tex]

finally,

s=100*5/8=62.5 [km/h].

The total heat supplied by the plant to convert the water to steam is 596.7 kcal.

Heat capacity is the quantity of heat required to raise the temperature of entire mass of a substance.

Q = Heat supplied to the water to the boiling point + Heat supplied to vaporize the water.

Q = mc₁Δθ + mc₂Δθ + mLv

where;

Substitute the given parameters and solve for the heat supplied in the process.

Q = (1)(1)(100 - 58.6) + (1)(0.48)(131.8 - 100)  + 540(1)

Q = 41.4 + 15.264 + 540

Q = 596.7 kcal

Thus, the total heat supplied by the plant to convert the water to steam is 596.7 kcal.

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The height of the cliff from the ground is 19.6 meters.

Projectile motion is the motion of an object thrown or projected into the air, subject to only the acceleration due to gravity.

Given is the initial speed of soccer ball kicked horizontally off a cliff which is 8 m/s. It cover a horizontal distance of 16 m. From this, we can write -

Horizontal initial velocity = u [h] = 8m/s

Horizontal distance covered = S [h] = 16m

For horizontal direction, of motion, we can write -

u [h] = 8m/s

S [h] = 16m

From second equation of motion applied for the horizontal direction -

S[h] = u[h] x t + 1/2 a[h] x t²

Since horizontal acceleration a[h] is zero, we can write -

t = S[h]/u[h]

t = 16/8

t = 2 seconds

Since the ball is kicked horizontally, the initial vertical velocity u[v] will be 0 m/s.

The acceleration in the vertical direction a[v] is directed vertically downwards and is equal to 9.8 m/s².

From second equation of motion applied for the vertical direction -

S[v] = u[v] x t + 1/2 x a[v] t²

S[v] = 1/2 x a[v] t²                      {u[v] = 0}

S[v] = 1/2 x 9.8 x 4

S(v) = 9.8 x 2

S[v] = 19.6 m

Therefore, the height of the cliff from the ground is 19.6 meters.

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[ The given question is not complete, the complete question is -

A soccer ball is kicked horizontally off a cliff with an initial speed of 8 m/s and lands 16 m from the base of the cliff: What is the time of flight of the soccer ball? What is the height of the cliff? ]

Answer:

6.0 m/s^2           There are 2 places of accuracy. (5.0 has only two places)

Explanation:

Formula

This uses the formula

a = (vf - vi)/t where

Solution

Substitute the givens into the formula

a = (50m/s - 20 m/s)/5

a = 30/5

a = 6 m/s^2

The characteristic that is used to measure light radiated by a star is luminosity. The correct option is C.

The radiant power emitted by a light-emitting object with respect to time is measured as luminosity, which is an absolute measure of radiated electromagnetic power.

The total amount of electromagnetic energy radiated per unit of time by a star, cosmos, or other celestial object is referred to as luminosity in astronomy.

The amount of light emitted by a star is measured using luminosity. It is the total amount of emery or light emitted by a star per unit of time. Or it is the total energy produced by a star in one second from its surface.

Thus, the correct option is C.

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Your question seems incomplete, the missing options are:

Size

color

luminosity

temperature

a. Her x position at t = 0.80 s is 0.0832 m

b. Her y position at t = 0.80 s is -28.8 m

c. Her x velocity component at t = 0.80s is 2.08 m/s

d. her y velocity component at t = 0.80s is -3.6 m/s

Since the skateboarder travels on a horizontal surface with an initial velocity of 3.6 m/s toward the south and a constant acceleration of 2.6 m/s² toward the east.

Now since she starts from the origin, to find her x position after 0.80 s, using the equation of motion for the x - components of motion,

x = ut + 1/2at² where

So, substituting the values of the variables into the equation, we have

x = ut + 1/2at²

x = 0 m/s × 0.8 s + 1/2 × 2.6 m/s² × (0.8 s)²

x = 0 m + 1.3 m/s² × 0.64 s²

x = 0 m + 0.832 m

x = 0.832 m

So, her x position at t = 0.80 s is 0.0832 m

Using the equation of motion for her y - components of motion, her y position is y = ut + 1/2at² where

So, substituting the values of the variables into the equation, we have

y = ut + 1/2at²

y = -3.6 m/s × 0.8 s + 1/2 × 0 m/s² × (0.8 s)²

y = -3.6 m × 0.8 s + 0

y = -28.8 m

So, her y position at t = 0.80 s is -28.8 m

Using the equation of motion for her x - component of motion, her x velocity compoent after t = 0.8 s is

v = u + at where

So, we have

v = u + at

v = 0 m/s + 2.6 m/s² × 0.8 s

v = 0 m/s + 2.08 m/s

v = 2.08 m/s

So, her x velocity component at t = 0.80s is 2.08 m/s

Using the equation of motion for her y - component of motion, her xyvelocity compoent after t = 0.8 s is

v = u + at where

So, we have

v = u + at

v = -3.6 m/s + 0 m/s² × 0.8 s

v = -3.6 m/s + 0 m/s

v = -3.6 m/s

So, her y velocity component at t = 0.80s is -3.6 m/s

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Answer:

The electrostatic interactive force between electrical charges is exactly the same as the gravitational interaction between them

Explanation:

The magnitude of charge is independent of the weight and displacement of the charge but only sign of the charge is the dependent factor.

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There are few points given to us in this question.

A) There are 1.41× 10^16 m in 1.5 light years

B) There are 9.4 × 10^4 AU in 1.5 light years

What is a light year?

Many might confuse it with time because of the presence of term “year” this term is actually used for space objects to measure distance. Light Year is the distance travelled by light in one Earth year.

It’s a term named by German scientist Friedrich Bessel who first used it in 1838.

One light year is about 6 trillion miles or 9.46 trillion kilometers.

To solve part A, we will first multiply V(light) with time (in seconds) in a year and multiply the product with 1.5 light year per light year.

Now let us understand what is Astronomical Unit AU?

AU is also used to measure distance but within our solar system. It is usually the average distance between Sun and Earth. It is about 93 million miles or 150 million kilometers.

To solve part B, we first convert the light year to AU and we do this by using the final value from part A and then convert it in significant figure to obtain a proper value for the answer.

The calculations are shown in the figures below.

Hence,

A) There are 1.41× 10^16 m in 1.5 light years

B) There are 9.4 × 10^4 AU in 1.5 light years

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The rocket ship rises to a height of 27.83 km above the launch pad after 94 seconds of flight.

We know that,

s = u t + 1 / 2 a t²

where,

s = Displacement

u = Initial velocity

a = Acceleration

t = Time

Given that,

u = 0

a = 6.3 m / s²

t = 94 s

s = 0 + 1 / 2 ( 6.3 * 94² )

s = 27833.4 m

s = 27.83 km

Displacement the distance between the initial point and final point. It is denoted using s.  

Therefore, the rocket ship rises to a height of 27.83 km above the launch pad after 94 seconds of flight.

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Answer:

2g cube of Aluminum

Explanation:

An auto's velocity increases uniformly from 6.0 m/s to 20 m/s while covering 70 m in a straight line, its acceleration is 2.6 [tex]m/s^2\\[/tex] and the time taken is 5.4 s.

The probable rate at which an object’s velocity changes with respect to time is referred to as its acceleration in mechanics. They are vector quantities and accelerations.

The direction of the net force acting on an object determines the direction of its acceleration.

The meter per second ([tex]m/s^2\\[/tex]) unit of acceleration is used to measure speed. The square meter is a measure of area ([tex]m^2[/tex])

The auto's velocity increases uniformly from 6m/s to 20m/s while it is covering the total of 70m.

Since it increases uniformly, thus we can use equation of motion

[tex]V^2 - U^2 =2as[/tex]

U = 6m/s

V = 20m/s

s = 70 m

Thus,

[tex](20)^2 - (6)^2 = 2*a*70[/tex]

a = 2.6 [tex]m/s^2\\[/tex]

Then for the time, we have

a = [tex]\frac{(V-U)}{t}[/tex]

2.6 = [tex]\frac{20 - 6}{t}[/tex]

t = 5.4 s

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The lenght of the missing side is 29.41 ft.

To calculate the missing length of the triangle, we use pythagoras theorem.

Pythagoras theorem states that in a right angle triangle, the square the hypotenus is equal to the sum of the square of the two other sides.

These can be expressed mathematically as

From the question,

Substitute these values into equation 1

Hence, the lenght of the missing side is 29.41 ft.

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Force = (mass) x (acceleration)

so

Acceleration = Force / mass

Acceleration = (1400 N) / (70 kg)

Acceleration = 20 m/s²

If a person swims at a constant speed of 1 meter per second, than the linear function will be used to model the distance travelled by the swimmer.

The parent function is "the principal's of ice"

A linear function is a function that forms a straight line on a graph. It is generally a polynomial function whose degree is at most 1 or 0. Although linear functions are also represented in terms of calculus and linear algebra.

Here Y-axis represents Distance and X-axis represents Time.

Also speed is the rate of change of distance with respect to time i.e. distance is changing linearly with time

Mathematically it is  [tex]Speed = \frac{distance}{time}[/tex].

Change in Distance = Change in time and hence speed is constant.

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The mass of the second rocket should be 0.4 kg in order for the acceleration to be half of the first rocket's acceleration.

We know that,

F = m a

where,

F = Force

m = Mass

a = Acceleration

Given that,

[tex]F_{1}[/tex] = 100 N

[tex]m_{1}[/tex] = 0.2 kg

[tex]F_{1}[/tex] = [tex]F_{2}[/tex] = 100 N

[tex]a_{2}[/tex] = [tex]a_{1}[/tex] / 2

[tex]F_{1}[/tex] = [tex]m_{1}[/tex] *  [tex]a_{1}[/tex]

[tex]a_{1}[/tex] = 100 / 0.2

[tex]a_{1}[/tex] = 500 m / s²

[tex]a_{2}[/tex] = 500 / 2

[tex]a_{2}[/tex] = 250 m / s²

[tex]m_{2}[/tex] = 100 / 250

[tex]m_{2}[/tex] = 0.4 kg

According to Newton's second law of motion, acceleration of an object is the result of force acting on the object.

Therefore, The mass of the second rocket should be 0.4 kg

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C.  The following scenarios that shows an object with a negative velocity and a negative acceleration is "a pig moves toward the reference point slowing down."

A negative velocity occurs when an object moves in the negative direction.

Example of negative velocity;

If the object is slowing down then its acceleration vector is directed in the opposite direction as its motion. Thus, the acceleration of the object will be negative.

Thus, the following scenarios that shows an object with a negative velocity and a negative acceleration is "a pig moves toward the reference point slowing down."

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The ball's velocity is 9.9 m/s fast when it hits the sidewalk.

Velocity is the rate of change of displacement.

To calculate how fast the ball was moving when it hits the sidewalk, we use the formula below.

Fromula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, the ball's velocity is 9.9 m/s fast when it hits the sidewalk.

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The ratio of the cubes of any two planets' average distances from the sun (r) to their squares representing their periods (T) is equal to one.

First Law: The sun is at the center of elliptical planetary orbits.

Second Law: Equal areas are covered in equal amounts of time by the radius vector from the sun to a planet.

Third Law: For every planet, the ratio of the cube of the ellipse semimajor axis to the square of the period of revolution is the same.

The third law of Kepler, also referred to as the Law of Harmonies, states that the ratio of any two planets' squared periods to their squared average distances from the sun is equal to one. The third law compares a planet's orbital radius and period to those of other planets.

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Answer:

Assuming the height at which the wrench was dropped is 336 feet,

the person will hear the sound in 0.3 sec and the wrench will hit the ground only after 4.58 seconds so there is enough time to get out of the way

Explanation:

Without knowing the exact height at which the 24th floor is located, it would be difficult to determine whether the wrench will hit the ground before the sound hits the ground

Realistically, we can assume each floor of the building is 14' high

So the height at which the 24th floor is located is 24 x 14 = 336 feet

To travel 336 feet at 1100 feet per second, sound will take 336/1100 seconds which is 0.30 second

Let's compute the time taken for the wrench to hit the ground

The acceleration due to gravity is usually taken to be 16 feet/second²

The displacement which is the distance traveled by an object with an initial velocity of u in time t is given by the equation:
s = ut + (1/2)t²

Here the initial velocity is 0

So the equation is
s = 1/2 x 32 x t² = 16t²

To cover 336 feet we substitute 336 for s and get

336 = 16t²

t² = 336/16

t = ±√(336/16) ≈ 4.58 seconds (we only take the positive root)

So the person will hear the sound in 0.3 sec and the wrench will hit the ground only after 4.58 seconds so there is enough time to get out of the way

In general, we can state that if the height from which the wrench was dropped is h then time t taken for wrench too hit the ground is

t = √(h/16) seconds

If this is greater than the time taken for sound to travel the same distance then the person can get out of the way

The person must climb the stairs about eight times.

We know that energy is the ability to do work. Work and energy are two quantities that are dimensionally similar to each other. In this case, we are trying to obtain the number of times that A 100.0 kg person will need to climb a 10.0 m stairway how many times to "work off" each excess 20 Cal (kcal) consumed.

Now;

Work done by the person = mgh =  100.0 kg  * 10 m/s^2 * 10 m = 10000 J

To convert from joules to kcal, we know that;

1 kcal = 4184 J

x =  10000 J

x = 1 kcal *  10000 J/4184 J

x = 2.39 kcal

In order to burn off the excess calories, the person must climb the stairs;

20 kcal/2.39 kcal = 8

The person must climb the stairs about eight times.

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The law of conservation of mass states that matter cannot be created or destroyed.

The law of conservation of mass states that the mass of the reactant must be equal to the mass of the product.

In 18th century law of conservation of mass was given by Levoisier.

It states that mass is neither created nor destroyed.

Example -

The law of conservation of mass states that matter cannot be created or destroyed.

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The ball rise 18.42 m from its original position.

Height is the vertical distance between two points.

To calculate the height of the ball, from the original position, we use the formula below.

Formula:

Make h the subject of the equation

Where:

From the question,

Substitute these values into equation 2

Hence, the ball rise 18.42 m from its original position.

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The distance covered by the runner after starting from rest is 39.74 m/s².

The real route length of a moving particle or object is referred to as distance. The shortest distance between a body's initial and final positions is referred to as displacement. Speed is the amount of distance a particle travels in one unit of time.

The constant acceleration of a runner is 1.1 m/s².

The runner maintains the constant acceleration for 8.5 seconds.

So,

a = 1.1 m/s²

t = 8.4 seconds

Since the runner starts from the rest.

Therefore, the initial velocity u = 0 m/s

Using the equation of motion,

s = ut + (1/2) × a × t²

s = 0 × 8.5 + ( 1/2 ) × 1.1 × 8.5 × 8.5

s = ( 1/2 ) × 79.475

s = 39.737 m/s²

s = 39.74 m/s²

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Answer:

B

Explanation:

Answer:

The precision corresponds to the least count of the measurements, which is 0.1 cm 0.1 c m for the length of the box. In a similar manner, the precision of the volume is 0.01×103 cm3=10 cm3 0.01 × 10 3 c m 3 = 10 c m 3 .

The perimeter of the pool is measured as 30 feet.

We know that a rectangle is a four sided polygon recall that a polygon is any figure that has n sides. The number of sides in a  polygon could move from three to infinity. The polygons come in different shapes and are solids with definite values of surface areas and volumes.

The rectangle is four sided which each of the angles of the rectangle adding up to give 360 degrees. It must be noted that the opposite sides of the rectangle are equal to each other.

We have the following information;

Length of the pool = 4(3 feet) = 12 feet

Width of the pool = 3 feet

Since perimeter = 2 ( length + width)

Perimeter = 2( 12 + 3)

Perimeter = 30 feet

Hence, the perimeter of the pool is measured as 30 feet.

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The value 35.6 have on the measures of central tendency for the data in the left column, as mean will be higher than the median and mode. The correct option is C.

The mean is the average of a set of values in mathematics and statistics. There are several ways to compute the mean, including the simple arithmetic mean, the geometric mean, and the harmonic mean.

To find the mean, add all of the numbers together. The total sum is then divided by the number of scores used. The mean or average of the number set in this example is 6.7.

The value 35.6 has a positive effect on the measures of central tendency for the data in the left column, as the mean is greater than the median and mode.

Thus, the correct option is C.

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277.01 picometers is equivalent to 2.7701 × 10-⁸ centimetres in scientific notation. Details about how to convert picometers to centimetres can be found below.

Picometers is the SI unit of length that is equal to 10−¹² meters.

On the other hand, centimetres is another S.I unit of length that is equal to 10-² metres.

The conversion factor of picometers to centimetres is as follows:

1 picometre = 1 × 10-¹⁰ centimetres

277.01 picometers is equivalent to 2.7701 × 10-⁸ centimetres

Therefore, 277.01 picometers is equivalent to 2.7701 × 10-⁸ centimetres in scientific notation.

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The metric conversion of the given quantities is determined as

Metric Conversion refers to the conversion of the given units to desired units for any quantity to be measured.

The metric conversion of the following quantities is calculated as follows;

5 KL = 5 x 1000 L = 5,000 L

3L = 3 x 1/1000 L = 0.003 KL

4g = 4 x 1/1000 g = 0.004 kg

81 kg = 81 x 1000 g = 81,000 g

52 dg = 52 x 1/10 g = 5.2 g

3 dm = 3 x /10 m = 0.3 m

14 mm = 14 x 1/1000 m = 0.014 m

Thus, the metric conversion of the given quantities is determined as

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