a car is moving at 2 m/s when it accelerates at 4 m/s^2 for 2 seconds. His new velocity is?

If the radius of a circle of area A and circumference C is doubled, the new circumference of the circle, in terms of C, will be equal to 2C.

The area (A) of a circle is given by:

\( A = \pi r^{2} \)   (1)

And a circumference (C) is:

\( C = 2\pi r \)   (2)

Where:

r: is the radius

If the radius of a circle and circumference is doubled, the new circumference of the circle is:

\( C_{2} = 2 (2 \pi r) = 2C \)

Therefore, the new circumference of the circle in terms of C is equal to 2C.

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According to the law of conservation of momentum,

Where,

We need v2f

Substituting the known values in the equation,

Simplyfing,

On rearranging the above equation we get,

i.e.

The negative sign indicates that the surfboard will move backward with a velocity of 2m/s after the surfer jumps off of it.

The magnitude of the equilibrant force is equal in magnitude but opposite in direction to the resultant vector R. Therefore, the magnitude of the equilibrant force is 500 dyne.

The correct answer is option D.

To find the magnitude of the equilibrant force, we need to determine the resultant of the two given forces and then find its opposite vector, which will be the equilibrant force.

Let's break down each force into its x-component and y-component:

For F1 = 300 dyne at an angle of 309° with the +x-axis:

F1x = F1 * cos(309°)

= 300 dyne * cos(309°)

= -259.8 dyne (negative because it is in the opposite direction of the positive x-axis)

F1y = F1 * sin(309°)

= 300 dyne * sin(309°)

= -150 dyne (negative because it is in the opposite direction of the positive y-axis)

For F2 = 400 dyne at an angle of 120° with the +x-axis:

F2x = F2 * cos(120°)

= 400 dyne * cos(120°)

= -200 dyne (negative because it is in the opposite direction of the positive x-axis)

F2y = F2 * sin(120°)

= 400 dyne * sin(120°)

= 346.4 dyne

Now, we can add the x-components and y-components separately:

Rx = F1x + F2x

= -259.8 dyne + (-200 dyne)

= -459.8 dyne

Ry = F1y + F2y

= -150 dyne + 346.4 dyne

= 196.4 dyne

The resultant vector R is given by:

R =\(\sqrt{(Rx^2 + Ry^2)}\)

= \(\sqrt{((-459.8 dyne)^2 + (196.4 dyne)^2)\\}\)

≈ 500 dyne

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Explanation:

it's 5 + 5 + 5 + 12 + 5 x 7 x 7 7+ 8 5+6+ +8 +9 + 9 5

The speed of the second marble must be 14.8 m/s so that the two marbles reach the ground at the same time.

The time taken by the first stone to reach the ground is calculated using the formula below:

h = ut + ¹/₂gt²

where:

From the data provided;

h = 30, u = 10m/s, g = 9.8 m/s

30 = 10t  + 0.5 * 9.8t²

30 = 10t + 4.9t²

4.9t² + 10t - 30 = 0

t = 1.65 s

For the second marble, time taken = 1.65 - 0.50

t = 1.15 s

Initial velocity, u will be:

30 = u(1.15)  + 0.5 * 9.8 * 1.15²

1.15u = 30 - 12.96

u = 14.8 m/s

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Each of the five friends needs to pay £12 to cover the cost of their own meals and contribute towards the birthday person's meal. Using mean allows us to distribute the cost equally among the friends, ensuring a fair division of expenses for the meal.

To determine how much each of the five friends needs to pay, we can use the concept of averages (mean) and divide the total cost by the number of people paying.

In this scenario, the total cost of the meal for 6 people is £12 per person. Since the other 5 friends have decided to pay for the birthday person's meal, they will collectively cover the cost of their own meals plus the birthday person's meal.

To calculate the total cost covered by the five friends, we can subtract the cost of one person's meal (since the birthday person's meal is being paid by the group) from the total cost. The cost of one person's meal is £12.

Total cost covered by the five friends = Total cost - Cost of one person's meal

= (£12 x 6) - £12

= £72 - £12

= £60

Now, to find out how much each of the five friends needs to pay, we divide the total cost covered by the five friends (£60) by the number of friends (5).

Amount each friend needs to pay = Total cost covered by the five friends / Number of friends

= £60 / 5

= £12

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According to the Law of Conservation of Mechanical Energy, if there are no external or non-conservative forces acting on a system (such as friction), then, the total mechanical energy of the system remains constant.

The mechanical energy of a system is the sum of its kinetic energy K and its potential energy U:

The kinetic energy of a particle with mass m and speed v is:

And the potential energy of a particle with mass m located at a height h is:

Where g is the acceleration of gravity on the surface of Earth.

When the roller coaster car is located at the top of the 30.00-meter hill, its kinetic energy is 0 and its potential energy is:

Then, the total mechanical energy of the roller coaster car is:

On the other hand, the potential energy of the car when it is halfway down is:

Since the total mechanical energy is the same, we can find the kinetic energy of the car when it is halfway down using the law of conservation of mechanical energy:

Therefore, the potential and kinetic energy of the car when it is halfway down the hill at a height of 15.0 meters are:

Using PE for potential energy and KE for kinetic energy:

Therefore, the correct choice is the second option.

The minimal SOP equation that implements the same logic as the given equation is f = ab + ac.

The sum of product (SOP) is a type of logic circuit used to represent a logical expression. It is also known as a canonical sum of products and is a type of canonical form. An SOP expression is composed of one or more product terms. Each product term is the logical AND of one or more literals and is separated from other product terms with a plus sign. The sum of product form of a logic expression is a sum of the product terms of the expression.

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Answer:

The distance traveled in 1 year is: \(3.143*10^{16}ft\)

Explanation:

Given

\(s = 982,080,000 ft/s\) --- speed

\(t = 32,000,000 s\) --- time

Required

The distance traveled

This is calculated as:

\(Speed = \frac{Distance}{Time}\)

So, we have:

\(Distance = Speed * Time\)

This gives:

\(Distance = 982,080,000 ft/s * 32,000,000 s\)

\(Distance = 982,080,000 * 32,000,000ft\)

\(Distance = 3.143*10^{16}ft\) -- approximated

Answer: 490

Explanation:

The dart experiences an impulse of larger magnitude during the collision. This is because the dart has less mass than the block, so the same amount of momentum change will result in a larger impulse.

Momentum is a physical concept that describes the tendency of an object to remain in motion with the same speed and direction unless it is acted on by an outside force. It is a measure of an object's inertia and is often expressed as the product of its mass and velocity. Momentum is a vector quantity, meaning that it has both magnitude and direction. Momentum is conserved in closed systems, meaning that the momentum before an interaction is equal to the momentum after the interaction. This is known as the law of conservation of momentum and can be used to solve many problems involving collisions and other interactions between objects.

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The angular deceleration of the ball is -0.42 rad/s².

Angular acceleration is a measure of the rate of change of angular velocity of an object rotating about an axis. When an object rotates, its angular velocity (ω) can change as a result of various factors, such as the application of an external torque or the redistribution of mass in the object.

We can use the formula for angular acceleration:

α = (ωf - ωi) / t

where

α is the angular acceleration

ωi is the initial angular velocity

ωf is the final angular velocity (which is zero in this case since the ball comes to a stop)

t is the time it takes for the ball to come to a stop

To find the initial and final angular positions, we can use the formula:

θf - θi = ωi * t + (1/2) * α * t²

where

θi is the initial angular position (0 in this case)

θf is the final angular position (90 radians in this case)

Substtuting the given values, we have:

θf - θi = ωi * t + (1/2) * α * t²

90 - 0 = (9.13 rad/s) * 15 s + (1/2) * α * (15 s)²

Simplifying and solving for α, we get:

α = -0.42 rad/s²

Therefore, the angular deceleration of the ball is -0.42 rad/s².

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The formula for calculating the energy of radiation is expressed as

E = hf

where

E is the energy

h is the planck constant = 6.626 x 10^-34

f is the frequency of the wave

From the information given,

Answer:

23.52(m/s) is the fastest it can go

The essence of the commercial is to draw the attention of the public to the products of a firm.

Commercials are the primary ways by which companies promote their products. The essence of the commercial is to draw the attention of the public hence the commercial is  designed with music graphics and other means that aid effective communication.

The commercial that got my attention is that of the United Bank for Africa owing to the beautiful blend of orchestra music used in the advertisement which appeals immediately to the mind. The advert targets the business class in the society and aims at granting soft credit to small and medium scale entrepreneurs. It conveys its message to the clientele via music. The advert can be regarded as a trend.

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Answer:

Step 1: List the mass and velocity of the object. Step 2: Convert any values into SI units (kg, m, s). Step 3: Multiply the mass and velocity of the object together to get the momentum of the object.

Answer:

1)   I_ pendulum = 2.3159 kg m² , 2)  I_pendulum = 24.683 kg m²

Explanation:

In this exercise we are asked to calculate the moment of inertia of a physical pendulum, let's start by calculating the center of mass of each elements of the pendulum and then the center of mass of the pendulum

Sphere

They indicate the density of the sphere roh = 37800 kg / m³ and its radius

r = 5 cm = 0.05 m

we use the definition of density

               ρ = M / V

               M = ρ V

the volume of a sphere is

                V = 4/3 π r³

we substitute

              M = ρ 4/3 π r³

we calculate

              M = 37800  4/3 π 0.05³

              M = 19,792 kg

Bar

the density is ρ = 32800 kg / m³ and its dimensions are 1 m,

0.8 cm = 0.0008 m and 4cm = 0.04 m

The volume of the bar is

               V = l w h

              m = ρ l w h

we calculate

              m = 32800 (1   0.008   0.04)

              m = 10.496 kg

Now we can calculate the center of mass of the pendulum, we use that the center of mass of the sphere is its geometric center, that is, its center and the center of mass of the bar is where the diagonals intersect, in this case it is a very bar. long and narrow, whereby the center of mass is about half the length. It's mass scepter of the pendulum is

               r_cm = 1 / M (M r_sphere + m r_bar)

               M = 19,792 + 10,496 = 30,288 kg

               r_cm = 1 / 30,288 (10,496 0.5 + 19.792 (1 + 0.05))

               r_cm = 1 / 30,288 (5,248 + 20,7816)

               r_cm = 0.859 m

This is the center of mass of the pendulum.

1) Now we can calculate the moment of inertia with respect to this center of mass, for this we can use the theorem of parallel axes and that the moments of inertia of the bodies are:

Sphere I = 2/5 M r2

Bar I = 1/12 m L2

parallel axes theorem

                  I = I_cm + m D²

where m is the mass of the body and D is the distance from the body to the axis of rotation

Sphere

      m = 19,792 ka

the distance D is

                D = 1.05 -0.85

                D = 0.2 m

we calculate

               I_sphere = 2/5 19.792 0.05 2 + 19.792 0.2 2 = 0.019792 +0.79168

               I_sphere = 0.811472 kg m²

Bar

m = 10.496 kg

distance D

             D = 0.85 - 0.5

             D = 0.35 m

              I_bar = 1/12 10.496 0.5 2 + 10.496 0.35 2 = 0.2186 + 1.28576

              I_bar = 1.5044 kg m²

The moment of inertia is a scalar quantity whereby the moment of inertia of the body is the sum of the moment of the parts

              I_pendulum = I_sphere + I_bar

              I_pendulum = 0.811472 +1.5044

              I_ pendulum = 2.3159 kg m²

this is the moment of inertia of the pendulum with respect to its center of mass located at r = 0.85 m

2) The moment is requested with respect to the pivot point at r = 0 m

Sphere

        D = 1.05 m

         I_sphere = 2/5 M r2 + M D2

        I_sphere = 2/5 19.792 0.05 2 + 19.792 1.05 2 = 0.019792 +21.82

        I_sphere = 21.84 kg m²

Bar

D = 0.5 m

      I_bar = 1/12 10.496 0.5 2 + 10.496 0.5 2 = 0.21866 + 2.624

      I_bar = 2,84266 kg m 2

The pendulum moment of inertia is

       I_pendulum = 21.84 +2.843

       I_pendulum = 24.683 kg m²

This moment of inertia is about the turning point at r = 0 m

The magnitude of the net force is 5.11 N and its direction is 5.59° counterclockwise from the +x-axis.

The x-component of the net force is 5.11 N, which is equal to the x-component of the first force.

To determine the magnitude and direction of the net force, we need to first add the x and y components of the two forces:

Fx = 15.0 N cos 68.0° = 5.11 N

Fy = -19.0 N + 18.5 N = -0.5 N

The net force is the vector sum of these two forces:

Fnet = sqrt[(5.11 N)^2 + (-0.5 N)^2] = 5.11 N

To find the direction of the net force, we can use trigonometry:

θ = tan^-1(Fy/Fx) = tan^-1(-0.5 N/5.11 N) = -5.59°

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Answer:

146.27 m

Explanation:

From the question given above, the following data were obtained:

Velocity of tourist (vₜ) = 4.65 m/s

Distance travelled by tourist (dₜ) = d

Velocity of bear (v₆) = 5.68 m/s

Distance travelled by bear (d₆) = 32.4 + d

Value of d =?

Next, we shall determine the time taken for tourist and the bear to get to the car.

For the tourist:

Velocity of tourist (vₜ) = 4.65 m/s

Distance travelled by tourist (dₜ) = d

Time (tₜ) =?

vₜ = dₜ / tₜ

4.65 = d/tₜ

Cross multiply

4.65 × tₜ = d

Divide both side by 4.65

tₜ = d / 4.65

For the bear:

Velocity of bear (v₆) = 5.68 m/s

Distance travelled by bear (d₆) = 32.4 + d

Time (t₆) =?

v₆ = d₆ / t₆

5.68 = (32.4 + d) / t₆

Cross multiply

5.68 × t₆ = (32.4 + d)

Divide both side by 5.68

t₆ = (32.4 + d) / 5.68

NOTE: Both the tourist and the bear have the same time. Thus, to obtain the value of d, we shall equate both the time taken for the tourist and the bear together. This is illustrated below:

Time taken by tourist (tₜ) = time taken by the bear (t₆)

tₜ = d / 4.65

t₆ = (32.4 + d) / 5.68

tₜ = t₆

d / 4.65 = (32.4 + d) / 5.68

Cross multiply

d × 5.68 = 4.65 (32.4 + d)

5.68d = 150.66 + 4.65d

Collect like terms

5.68d – 4.65d = 150.66

1.03d = 150.66

Divide both side by 1.03

d = 150.66 / 1.03

d = 146.27 m

Thus, the maximum value of d is 146.27 m

A 43-kg rock is dropped from a 36 m, experiencing a Uniformly Accelerated Motion and falling to the ground 2.7 s later.

A Uniformly Accelerated Motion is a motion in which the acceleration of the object is constant.

A 43 kg rock is dropped from a 36 m tower. Given the only acceleration is that of gravity, we can calculate the time required to hit the ground using the following kinematic equation.

s = 1/2 × a × t²

t = √(2s / a)

t = √[2 × 36 m / (9.8 m/s²)] = 2.7 s

where,

A 43-kg rock is dropped from a 36 m, experiencing a Uniformly Accelerated Motion and falling to the ground 2.7 s later.

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Answer:

Condensation

Explanation:

Answer:When water changes from a gas in the atmosphere to a liquid droplet in a cloud, this is known as

Group of answer choices

transpiration

condensation

evaporation

precipitation,←, that one is right

Explanation: so ur answer is precipitation

Answer:

E. Some charges in the region are positive, and some are negative.

Explanation:

Electric potential is given as;

\(V = \frac{W}{Q}\)

where;

W is the work done in moving a charge between two points which have a difference in potential

Q is quantity of charge in the given region

If the electric potential at a given point in the region is zero, then sum of the charges in the given region must be equal to zero. For the charges to sum to zero, some will be positive while some will be negative,.

Therefore, the correct statement in the given options is "E"

E. Some charges in the region are positive, and some are negative.

Answer:

-48cm

Explanation:

For a convex lens f is +ve and V is +ve

Using the formula 1/f=1/v+1/u

u=12cm and f=16cm

1/16-1/12=1/v

1/v=-1/48

v=-48cm

Answer: D

Explanation:

Answer

Explanation

Hope it help you

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Answer:Liquid water is denser than Ice.

Ice float on top of liquid water.

Explanation:

Just trust me

The average speed of the baseball is  option  a. 40 m/s .

To calculate the average speed of the baseball, we use the formula:

Average Speed = Distance / Time

Given:

Distance = 18.4 m

Time = 0.46 s

Plugging in the values, we have:

Average Speed = 18.4 m / 0.46 s = 40 m/s

Therefore, the average speed of the baseball is 40 m/s.

Option a, 40 m/s, is the correct answer. This means that the baseball traveled an average distance of 40 meters per second from the pitcher's mound to home plate.

Average speed is a scalar quantity that represents the total distance traveled divided by the total time taken. It gives us an idea of how fast an object is moving on average over a given distance.

In this case, the baseball covered a distance of 18.4 meters in a time of 0.46 seconds. Dividing the distance by the time gives us the average speed of 40 m/s.

It's important to note that average speed is a measure of the overall rate of motion and does not provide information about the direction of motion. Therefore, negative values such as option b (-40 m/s) or extremely small values such as option c (0.03 m/s) are not appropriate in this context.

Option d (8.5 m/s) is also incorrect as it does not match the calculated average speed of 40 m/s.

Therefore, the correct answer is option a, 40 m/s, as it accurately represents the average speed of the baseball.

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Beth’s hygrometer is reading a temperature of 30°C and a relative humidity of 65%. The humidity in the air is 19.5 grams/cubic meter.

The actual vapor density or humidity can be determined from the relative humidity value and the saturation vapor density.

The formula that relates the actual vapor density or humidity, the relative humidity, and the saturation vapor density is given below:

Hence, the actual vapor density can be calculated as follows:

Actual vapor density or humidity = relative density * saturation vapor density / 100

From the graph;

saturation vapor density at 30°C = 30 g/cm³

relative humidity = 65%

Humidity = 65 * 30 / 100

Humidity = 19.5 g/cm³

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The best description of a well-designed testable question is "The question is clearly stated, the question can be tested in an experiment, and the results can be measured".

This type of question is the one that focuses on facts and aims at testing a hypothesis.

Some features include:

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Answer:

b

Explanation: