When the driver in the car moving with a speed of 15 ms-1 increases the
speed at a constant rate of 5 ms-2 . Calculate the speed attained by the
car, at the end of 5 s.

if the values of mass (m) and radius (R) are provided, the moment of inertia of the body about an axis through the center of disk A can be calculated as (3/2) * m * R^2, and the kinetic energy of the rotating body would be 162 * m * R^2 Joules.

To calculate the moment of inertia of the body about an axis through the center of disk A, we need to consider the moment of inertia contributions from each individual disk and add them up.

Let's denote the moment of inertia of each disk as I_A, I_B, and I_C, respectively. The moment of inertia of a disk rotating about its center can be calculated using the formula:

I = (1/2) * m * r^2

Where m is the mass of the disk and r is its radius.

Since the struts have negligible weight, we can assume that each disk has the same mass.

Let's assume the mass of each disk is m and the radius of each disk is R.

The moment of inertia of disk A (I_A) is given by:

I_A = (1/2) * m * R^2

The moment of inertia of disk B (I_B) and disk C (I_C) will be the same since they have the same mass and radius:

I_B = I_C = (1/2) * m * R^2

The total moment of inertia of the body about the axis through the center of disk A (I_total) is the sum of the individual moment of inertias:

I_total = I_A + I_B + I_C

= (1/2) * m * R^2 + (1/2) * m * R^2 + (1/2) * m * R^2

= (3/2) * m * R^2

To calculate the kinetic energy of the rotating body, we can use the formula:

Kinetic Energy = (1/2) * I_total * ω^2

Substituting the given values:

Kinetic Energy = (1/2) * ((3/2) * m * R^2) * (6.0 rad/s)^2

Simplifying further, if the values of m and R are given, we can calculate the moment of inertia and kinetic energy.

Assuming that the values of mass (m) and radius (R) are given, we can calculate the moment of inertia (I_total) and kinetic energy.

For the given values of ω = 6.0 rad/s and the previously calculated I_total:

I_total = (3/2) * m * R^2

Kinetic Energy = (1/2) * I_total * ω^2

= (1/2) * [(3/2) * m * R^2] * (6.0 rad/s)^2

= (9/2) * m * R^2 * (36.0 rad^2/s^2)

= 162 * m * R^2 Joules

Therefore, if the values of mass (m) and radius (R) are provided, the moment of inertia of the body about an axis through the center of disk A can be calculated as (3/2) * m * R^2, and the kinetic energy of the rotating body would be 162 * m * R^2 Joules.

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The maximum bending stress in the beam can be calculated using the equation: σmax = Mc/I

A statement claiming the equivalence of two expressions is known as an equation. It is typically expressed using mathematical symbols, and can be used to solve for unknown values. An equation can also be used to describe any physical or logical relationship between two or more items. Equations often involve variables, which are symbols that represent unknown values, and can help to express the behavior of a system.

Where M is the moment at the point where the stress is to be calculated, c is the distance from the neutral axis to the point where the stress is to be calculated, and I is the second area moment of inertia of the beam.
For a rectangular beam with a base of 3 inches and a height of 6 inches, the second area moment of inertia is I = (3*6^3)/12 = 27 in^4
Assuming the support at B exerts a uniformly distributed reaction on the beam, the maximum bending moment M = (Reaction * Length^2)/8 = (500 * 6^2)/8 = 1,875 in-lb.
Therefore, the maximum bending stress in the beam is σmax = (1,875 * 6)/27 = 350 psi.

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The approximate number of taste buds that humans have is 10,000 (option C).

Tastebuds are any of the small organs on the tongue used for tasting.

Taste buds are cells on the tongue that allow one to perceive tastes, including sweet, salty, sour, bitter and umami.

Taste buds regenerate approximately every 10 days, which means injured taste buds usually repair on their own. The average adult human has between 2000 and 8000 tastebuds.

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Answer:

We are given:

V1 = 5.5L          T1 = -38 C   or   235 k

V2 = 1.3L           T2 = T

From the gas equation:

PV = nRT

Since the pressure (P) , number of moles (n) and the universal gas constant (R) are constants, we can write the same equation as:

V / T = k  (where k is a constant)

so a bit more insight, since the values noted above are constant, when multiplied by each other, they will provide us with a constant number irrespective of the value of the variables

Changing the variables for the first case:

V1 / T1 = k   (where k is the same constant) ----------------(1)

Similarly,

V2 / T2 = k  (again, k has the same value)----------------(2)

From (1) and (2):

k is the common value

V1 / T1 = V2 / T2

Replacing the variables

5.5 / 235 = 1.3 / T

T = 1.3 * 235 / 5.5

T = 55.54 k

Therefore, at 55.54 K the gas will have a volume of 1.3L

If the Earth were seven times as massive as it is and its radius were five times its present value, your new weight will 218.4 N.

Your weight is the measure of force of gravity on you. So weight depends on the value of acceleration due to gravity.

W = mg

where;

The formula for acceleration due to gravity is given as;

g = ( GM ) / ( R² )

where;

If the Earth were seven times as massive as it is and its radius were five times its present value, the new acceleration due to gravity will be calculated as;

g' = ( G x 7M ) / (5R)²

g' = ( 7 / 25 ) ( GM / R² )

g' = 7/25 (g)

So the new acceleration due to gravity will reduce by a factor 7/25, and same will happen to your initial weight.

new weight = 7/25 x 780 N = 218.4 N

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Answer: The amount of time the force is applied.

Explanation:

The other variable along with the force which is used to calculate the impulse is the amount of time the object is in motion. Hence, option B is correct.

A force's overall impact as it operates across time is quantified by the term "impulse." It is often written in Newton seconds and given the symbol, J end text, and value.

This is similar to a shift in momentum, as we previously saw (p). The impulse-momentum theorem refers to this correspondence. We can directly connect the way a force applies to an object over time and the way that force affects the motion of an object according to the impulse-momentum theorem.

Because forces are frequently not constant in reality, impulse is necessary and beneficial. People- and engine-related forces start out at zero and gradually increase over time, however they can vary depending on a variety of circumstances.

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Answer:

they are closer!!

Explanation:

Hope this helped!! :D

Answer:

75 cm/second.

Explanation:

Formula:

Walking speed = stride length / time per step

Walking speed = 90cm/time per step

                         = 90cm/1.2 seconds (a common estimate time per step)

                         = 75cm/second.

The reason why this is needed is because a rocket with more mass is going to speed up slower. This happens due to the rocket being up in the air, and the force of gravity is now acting in the opposite direction of thrust, so now the amount of thrust that is pushing the rocket upwards is decreased. As well as that, you now have to increase the amount of upwards thrust to counteract this. For Example, the Saturn V rocket engine.

Answer:

  a) about 14.577 kg

  b) 300 N

Explanation:

b) In order for the acceleration to be the same for each mass, the 800 N force must be divided between the boxes in proportion to their mass. That is, the net force on the 5M mass must be 5/8 of the total force, or 500 N. Then the tension in the rope is 800 N -500 N = 300 N, which is 3/8 of 800 N.

Tension: 300 N

__

a) The total mass is 8M, and the total normal force on the floor is ...

  F = ma = (8M)(9.8 m/s^2)

The friction force is 0.7 times this, and is equal to the 800 N force pulling on the boxes.

  800 N = (8M)(9.8 m/s^2)(0.7)

  M = 800/(8·9.8·0.7) kg ≈ 14.577 kg

The electron number cannot be used instead because electrons can be removed from or added to an atom (option C)

The element of an atom is determined by its proton count, while the electron count can exhibit variability. Take, for instance, a sodium atom, which encompasses 11 protons and 11 electrons. However, it has the capacity to relinquish one electron, transforming into a sodium ion housing only 10 electrons.

This occurs due to the relatively loose binding of electrons to the nucleus, enabling their removal through the influence of an electric field or alternative mechanisms.

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\(\\ \bull\sf Frequency=f=6\times 10^{14}Hz\)

\(\\ \bull\sf Wavelength=\lambda=3.75\times 10^{-7}m\)

Now

\(\\ \sf\longmapsto v=f\lambda\)

\(\\ \sf\longmapsto v=6\times 10^{14}s^{-1}\times 3.75\times 10^{-7}m\)

\(\\ \sf\longmapsto v=22.5\times 10^7ms^{-1}\)

Answer:

velocity=v = 22.5 * 10⁷ m s ^ - 1

Explanation:

\(\sf\longmapsto \: Frequency = 6 * 10 ^ {14 } H z\)

\(\sf\longmapsto \: Wavelength = 3.75 \times 10 {}^{-7} m\)

Now let's solve out!!

\(\sf\longmapsto \: velocity = frequency \lambda\)

\(\sf\longmapsto \: velocity=6 \times 10 {}^{14} s {}^{ - 1} \times \ 3.75 \times 10 {}^{ - 7} m\)

\(\sf\longmapsto \: velocity= 22.5 \times 10 ^ 7 m s ^ { - 1}\)

Note:

\(\lambda\) is the Greek letter known as lambda.

Given that the mass of the object is m = 5kg.

The force on the object is F = 100 N.

The radius of the circle is r = 6 m

We have to find velocity.

Velocity can be calculated by the formula

Substituting the values, the velocity will be

Thus, the velocity is 10.95 m/s

To calculate the resultant force on the aircraft as it accelerates from the catapult, we can use the work-energy principle, which states that the work done on an object is equal to the change in its kinetic energy.

Since all of the kinetic energy at take-off is from the work done on the aircraft by the catapult, we can equate the work done by the catapult to the kinetic energy of the aircraft at take-off, that is:

Work done by catapult = kinetic energy of aircraft at take-off

The work done by the catapult is given by the force provided by the catapult multiplied by the distance over which it acts, that is:

Work done by catapult = force × distance

The distance over which the force provided by the catapult acts is given as 150 m, so we have:

Work done by catapult = force × 150

The kinetic energy of the aircraft at take-off is given by:

(1/2) × mass × velocity^2

Since the aircraft is initially at rest, its initial velocity is zero, so we have:

kinetic energy of aircraft at take-off = 0.5 × mass × (final velocity)^2

Using the work-energy principle, we can equate the two expressions for work done and kinetic energy, that is:

force × 150 = 0.5 × mass × (final velocity)^2

Solving for force, we get:

force = 0.5 × mass × (final velocity)^2 / 150

Therefore, the resultant force on the aircraft as it accelerates is given by:

force = 0.5 × mass × (final velocity)^2 / 150

Note that we need to know the mass and final velocity of the aircraft in order to calculate the resultant force.

The contact force (in N) between each pair of boxes is mathematically given as

F_{ab} = 3.56 N

F_{bc} = 1.2 N

Generally, Any force that is generated as a consequence of two objects coming into touch with one another is referred to as a contact force. Contact forces are present everywhere and are the cause of the vast majority of macroscopic groupings of matter's obvious interactions with one another.

In conclusion, The equation for is  Acceleration of the system is mathematically given as

a = 8.25 / (5.85 + 2.95 + 1.50)

a= 0.8 m/s^2

Therefore

F_{ab} = (Mb + Mc)*a

F_{ab} = (2.95 + 1.50) * 0.8

F_{ab} = 3.56 N

F_{bc} = Mc * a

F_{bc}= 1.5 * 0.8

F_{bc} = 1.2 N

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Answer:

the principal energy level is d because electrons are 2 times more

Two, four, eight and sixteen cells are produced from first, second, third and fourth cell division respectively.

When the body cell passes through cell division process, it divides into two daughter cells. In the second cell division, two cells divides into four cells. In the third cell division, the four cells divides into eight cells. In the fourth cell division, the eight cells divides and sixteen cells are produced.

So we can conclude that two, four, eight and sixteen cells are produced from first, second, third and fourth cell division respectively.

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The force acting on the particle at t = 1 s is 24.4 N.

Mass of the particle, m = 2 units

Distance of the curve, r(t) = (4t²- t³)i - 5tj + (t⁴- 2)k

The velocity of the particle,

v = d[r(t)]/dt = (8t - 3t²)i - 5j + 4t³k

The acceleration of the particle,

a = d²[r(t)]/dt² = (8 - 6t)i + 12t²k

Let the time for which the force is acting be 1 second.

Therefore, acceleration at t = 1 is,

a₁ = 2i + 12k

Hence, the magnitude of acceleration,

|a₁| = √(2²+ 12²)

|a₁| = √148

|a₁| = 12.2 unit/s²

Therefore, the force acting on the particle at t = 1 s is,

F₁ = m x |a₁|

F₁ = 2 x 12.2

F₁ = 24.4 N

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Answer:

Explanation:

The horizontal velocity is 1.61.

It is true that the  light is 15.000 more dangerous than the radiation of a microwave.

The wavelength shows the extent or how far the wave travels. Now we know that the energy of the wave can be use to find out how much dangerous the wave is.

Now;

1.6 * 10^-19 J = 1eV

x J = 1.8 eV

x = 1.8 eV * 1.6 * 10^-19 J /1eV

x = 2.88 * 10^-19 J

Now if the energy of the microwaves is 1.2 x 10^-4 J, then it follows that;

2.88 * 10^-19 J/ 1.2 x 10^-4 J,

= 2.4 * 10^15

Hence, it is true that the  light is 15.000 more dangerous than the radiation of a microwave.

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Answer:

The  value is  \(a = - 4.45 m/s^2\)

Explanation:

From the question we are told that  

       The  initial speed is  \(u = 28 \ m/s\) at a distance of  \(s_1 = 0 \ m\)

        The  final speed is  \(v = 0 \ m/s\)    at a distance of  \(s_2 = 88 \ m\)

Generally  from the  kinematic equation we have that

       \(v^2 = u^2 +2as\)

=>   \(a = \frac{v^2 - u^2 }{ 2(s_2 - s_1 )}\)

=>  \(a = \frac{0 - 28^2 }{ 2(88 - 0 )}\)

=>   \(a = - 4.45 m/s^2\)

The negative sign shows that it is decelerating

The velocity vector is always tangential to the motion path for a particle with curvilinear motion. The velocity of a particle describes the rate of change of its position over time and its direction is always tangent to the path of the particle's motion.

The acceleration vector describes the rate of change of the velocity and its direction can be either tangential or normal to the motion path, depending on whether the particle is changing speed or direction.

Yes, vectors and scalars are different. A scalar is a physical quantity that has only magnitude and no direction. A vector, on the other hand, is a physical quantity that has both magnitude and direction, such as velocity, force, or displacement.

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Answer:

False

Explanation:

Because that is not true

Answer:

0.5 m/s north

Explanation:

Take east to be +x, west to be -x, north to be +y, and south to be -y.

His displacement in the x direction is:

x = 20 m − 20 m = 0 m

His displacement in the y direction is:

y = 10 m

His total displacement is therefore 10 m north.

His velocity is equal to displacement divided by time.

v = 10 m north / 20 s

v = 0.5 m/s north

South

Explanation:

The magnetic force F on a point charge moving with a velocity v in the presence of a magnetic field B is given by

\(\vec{\textbf{F}} = q\vec{\textbf{v}}\textbf{×}\vec{\textbf{B}}\)

and according to the right-hand rule, an upward magnetic force on a proton moving westward is only possible if the magnetic field is directed southward.

Answer:

Explanation:

Net torque is calculated by multiplying the force with distance from the point of application of force to the point of pivot .

If more than 2 forces are present, then we either subtract the product of forces with their respective distances from pivot point or we add them . It depends on whether they both are present on opposite sides of pivot or on same side of pivot .

When a force is applied directly to the pivot point of balance, then the torque on due that force = 0 (zero) .

It is so because the torque is defined as the product of force and perpendicular distance from the pivot point but here the distance is 0 , therefore torque is zero.

The load impedance ZL must be equal to the complex conjugate of the Thevenin impedance ZTh for maximum average power transfer. This indicates that the load impedance (or resistance) must be equal to the magnitude of the Thevenin impedance for the highest average power transfer to a fully resistive load.

How is the average amount of energy absorbed determined?

As a result, the total power used by a circuit over the course of one full cycle is the sum of the power saved and the power returned.

How do you calculate average power?

The formula for average power in mathematics is: Average power = Total energy consumed Average amount of time spent P = W t.

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Answer:

Explanation:

Using the Newtons law of motion;

\(\sum Fx = ma_x\\Fm - Ff = ma_x\)

Fm is the moving force = 400N

Ff is the frictional force = μR

μ is the coefficient of kinetic friction

R is the reaction = mg

m is the mass

a is the acceleration

The equation becomes;

\(Fm - \mu R = ma_x\\Fm - \mu mg = ma_x\\400- \mu (25)(9.8) = 25(9)\\400 - 254.8 \mu = 225\\- 254.8 \mu = 225 - 400\\- 254.8 \mu = -175\\ \mu = \frac{-175}{- 254.8} \\\mu = 0.69\)

Hence the coefficient of kinetic friction between the box and floor is 0.69

The coefficient of kinetic friction between the box and the floor is 0.714.

Friction: This can be defined as the force that tends to oppose two surfaces in motion.

The question above can be solved using the formula

F-ma = mgμ................. Equation 1

Where F = Force applied to push the box, m = mass of the box, a = acceleration of the box, μ = coefficient of kinetic friction, g = acceleration due to gravity.

make μ the subject of the equation

μ = (F-ma)/mg................ Equation 2

From the question,

Given: F = 400 N, m = 25 kg, a = 9 m/s²,

Constant: g = 9.8 m/s²

Substitute these values into equation 2

μ = [400-(25×9)]/(25×9.8)

μ = (400-225)/245

μ = 175/245

μ = 0.714

Hence, the coefficient of kinetic friction between the box and the floor is 0.714.

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