A race car driver travelling at 15m*s^-1 accelerates at a constant value for 10.0s. She is now driving at a speed of 35 m*s^-1 What was her acceleration? Give your answer in m*s^-2 to one significant figure . Do not include units with your answer.

The centripetal acceleration of a point 0.100 m from the center when the wheel is moving at an angular speed of 12.0 rad/s is 1.44 m/s^2.

To find the centripetal acceleration of a point on the grinding wheel, we can use the formula:

a = rω^2

Where:

a is the centripetal acceleration,

r is the distance from the center of the wheel to the point, and

ω (omega) is the angular speed.

Given:

Radius of the grinding wheel, r = 0.150 m

Angular speed, ω = 12.0 rad/s

Distance from the center, r' = 0.100 m

First, we calculate the centripetal acceleration at the given angular speed:

a = (0.150 m)(12.0 rad/s)^2 = 21.6 m/s^2

Now, to find the centripetal acceleration at a distance of 0.100 m from the center, we substitute the new radius into the formula:

a' = (0.100 m)(12.0 rad/s)^2 = 1.44 m/s^2

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Answer:

Net force = 15 N

Explanation:

Given that,

Applied force on an object = 20 N

Frictional force = 5 N

We need to find the net force acting on the object.

Friction is an opposing force. It acts in the opposite direction.

Net force = Applied force - Frictional force

= 20 N - 5 N

= 15 N

Hence, the net force acting on the object is 15 N.

Answer:

True

Explanation:

Answer:

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Answer:-7.5

Explanation:

i just did it

The height that will illustrate the distance will be d = 6.36m

Based on the information given, the length of the vine will be:

L = ✓(16² + 27.7)²

L = 32m

The velocity of Jane when she reaches position B will be:

V = ✓2gh

V = ✓(2 × 9.8 × 4.3)

V = 9.18m/s

We will apply the conversation of momentum. This will be:

50 × 9.18 = (50 + 80)V1

V1 = 3.53m/s

Therefore, the height that will illustrate the distance will be:

31.36² + d² = 32²

d² = 32² - 31.36²

d = 6.36m

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Answer:

Explanation:

To solve this problem, we can use the following equations for the addition of two sinusoidal waves:

y1 = A1 sin(ωt + φ1)

y2 = A2 sin(ωt + φ2)

where A1 and A2 are the amplitudes of the waves, ω is the angular frequency, t is time, and φ1 and φ2 are the initial phase angles.

(a) To find the resultant amplitude of the two waves, we can use the following equation:

Ar = √(A1^2 + A2^2 + 2A1A2cos(φ2 - φ1))

where Ar is the resultant amplitude.

Substituting the given values, we get:

Ar = √((3.0 × 10^(-6))^2 + (4.0 × 10^(-6))^2 + 2(3.0 × 10^(-6))(4.0 × 10^(-6))cos(150° - 60°))

Ar ≈ 5.03 × 10^(-6) m

Therefore, the resultant amplitude is approximately 5.03 × 10^(-6) m.

(b) To find the resultant's initial phase angle, we can use the following equation:

tan(φr) = (A1sin(φ1) + A2sin(φ2))/(A1cos(φ1) + A2cos(φ2))

where φr is the initial phase angle of the resultant wave.

Substituting the given values, we get:

tan(φr) = (3.0 × 10^(-6)sin(60°) + 4.0 × 10^(-6)sin(150°))/(3.0 × 10^(-6)cos(60°) + 4.0 × 10^(-6)cos(150°))

φr ≈ 142.85°

Therefore, the resultant's initial phase angle is approximately 142.85°.

(c) The circle of reference and the time graph for the sine waves can be drawn as follows:

Sine Waves

The blue and red arrows represent the maximum displacement of the waves. The black arrow represents the displacement of the resultant wave. The time graph shows the displacement of each wave and the resultant wave over time.

Answer:

In a material, the magnetic behavior depends on the alignment of magnetic moments of the atoms. Magnetic moments are generated by the motion of the electrons in the atoms. When the magnetic moments of atoms in a material are aligned in a specific pattern, it creates a magnetic field which results in the material being magnetic.

In many materials, the magnetic behavior arises due to the alignment of magnetic domains, which are regions of atoms with magnetic moments aligned in the same direction. When many domains with aligned magnetic moments are present in a material, the material becomes magnetic.

The magnetic behavior of a material depends on the number of electrons and the arrangement of those electrons in the atoms. In particular, for an atom to have a magnetic moment, it must have unpaired electrons, meaning electrons that are not paired with another electron with the opposite spin. When these unpaired electrons in the atoms are aligned, they generate a magnetic moment. If all electrons are paired, there will not be a net magnetic moment, so the material will not be magnetic.

So, in summary, the magnetic behavior of a material is determined by the alignment of magnetic moments of atoms. When the magnetic moments of many atoms in a material align in the same direction, it creates a magnetic field, leading to a material being magnetic. This alignment is usually present in magnetic domains consisting of atoms with unpaired electrons.

The diameter of the smaller end of the pipe is approximately 0.78 meters.

To determine the diameter of the smaller end of the pipe, we can use the principle of conservation of mass. According to this principle, the mass flow rate of water should remain constant throughout the pipe.

The mass flow rate is given by the equation:
Mass flow rate = density of water * cross-sectional area * velocity

Since the density of the water remains constant, we can write:
Cross-sectional area1 * velocity1 = Cross-sectional area2 * velocity2

Given that the velocity1 is 13 m/s, the diameter1 is 1.2 m, and the velocity2 is 30 m/s, we can solve for the diameter2 using the equation:
(pi * (diameter1/2)^2) * velocity1 = (pi * (diameter2/2)^2) * velocity2

Simplifying the equation:
(1.2/2)^2 * 13 = (diameter2/2)^2 * 30

Calculating the equation:
(0.6)^2 * 13 = (diameter2/2)^2 * 30

0.36 * 13 = (diameter2/2)^2 * 30

4.68 = (diameter2/2)^2 * 30

Dividing both sides by 30:
0.156 = (diameter2/2)^2

Taking the square root of both sides:
0.39 = diameter2/2

Multiplying both sides by 2:
0.78 = diameter2

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Answer:

The answer is a fixed pulley

Answer:

t = Δa / v

Explanation:

To know which option is not true, we shall fine a relationship between acceleration (a), velocity (v), time (t) and radius (r). This is illustrated below:

Acceleration can simply be defined as the rate of change of velocity with time. Mathematically, it is expressed as shown below:

Acceleration = change in velocity / time

a = Δv / t ..... (1)

But

Δv = v₂ – v₁

Substitute the value of Δv into equation (1)

a = Δv / t

a = v₂ – v₁ / t ....... (2)

From equation (1), make Δv the subject of the equation.

a = Δv / t

Cross multiply

Δv = at .... (3)

From equation (1), make t the subject of the equation.

a = Δv / t

Cross multiply

at = Δv

Divide both side by a

t = Δv /a ...... (4)

From circular motion, centripetal's force is given by:

F = mv²/r

F = ma꜀

Therefore,

ma꜀ = mv²/r

Cancel out m

a꜀ = v²/r

SUMMARY:

a = Δv / t

a = v₂ – v₁ / t

Δv = at

t = Δv /a

a꜀ = v²/r

Considering the options given in question above, t = Δa / v is not a true statement.

Answer:

Option 4

Explanation:

Explanation:

Einsteins theory of relativity explains how space and time are linked for objects that are moving at a consistent speed in a straight line.

If the wave slows down with no change in frequency, the wavelength decreases.

A wave is defined as the disturbance that has the ability to transfer energy from one point to another in a medium.

The properties of a wave include the following:

When there is a change in the speed of the wave with no change in frequency, the length of the wave would decrease.

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( a) The acceleration of the box in the absence of friction is 8.49 m/s².

(b) The acceleration of the box in the presence of friction is 1.7 m/s².

(c) The speed of the box at the bottom of the incline is 18.44 m/s.

The acceleration of the box if no friction is present is calculated by applying Newton's second law of motion.

mg cosθ = ma

g cosθ = a

where;

The acceleration of the box in the absence of friction is calculated as;

a = ( 9.8 ) x ( cos 30 )

a = 8.49 m/s²

The acceleration of the box in the presence of friction is calculated as;

Ff = ma

where;

μmg cosθ = ma

μg cosθ = a

( 0.2 x 9.8 x cos 30 ) = a

1.7 m/s² = a

The speed of the box at the bottom of the incline is calculated as follows;

v² = u² + 2ah

where;

v² = 0 + 2ah

v = √ ( 2ah )

h = L sinθ

v = √ ( 2 x a x L sinθ )

v = √ ( 2 x 1.7 x 200 x sin 30 )

v = 18.44 m/s

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Given:

The rate of decay,

The initial mass, M=150 g

To find:

The expression for the mass at any time t.

Explanation:

On rearranging the given equation,

On integrating the above equation,

Final answer:

Thus the expression for the mass at any time t is

Therefore the correct answer is option A.

Answer:

50\(\sqrt{3}\)

Explanation:

As the force makes an angle 60 degree with y axis , the horizontal component (along x axis) will be 100sin(60) = 50\(\sqrt{3}\)

The gauge pressure of the water at the exit end of the pipe is -1281.125 kPa. Note that the negative sign indicates that the pressure is below atmospheric pressure, as gauge pressure is measured relative to atmospheric pressure.

What is Atmospheric Pressure?

Atmospheric pressure, also known as air pressure, is the force per unit area exerted by the weight of the Earth's atmosphere on a surface. It is the pressure exerted by the air molecules in the Earth's atmosphere due to their gravitational attraction towards the center of the Earth. Atmospheric pressure is caused by the weight of the air above a given surface pressing down on it.

To solve this problem, we can apply Bernoulli's equation, which relates the pressure, velocity, and height of a fluid flowing through a pipe.

We can start by calculating the velocity at the exit using the equation of continuity, which states that the mass flow rate of an incompressible fluid remains constant along a streamline:

Substituting the given values:

\(V^{2}\) = (0.025\(m^{2}\) * 2.5 m/s) / 0.010 \(m^{2}\)

\(V^{2}\) = 62.5 m/s

Now, we can substitute the known values into Bernoulli's equation to find the gauge pressure at the exit:

\(P^{2}\)= P1 + (1/2)ρ(\(v1^{2}\) - \(v2^{2}\))

\(P^{2}\)= 46 kPa + (1/2) * 1000 kg/m^3 *\((2.5 m/s)^{2}\) - \((62.5 m/s)^{2}\)

\(P^{2}\) = 46 kPa + 625 kPa - 1953.125 kPa

\(P^{2}\) = -1281.125 kPa

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Answer:

Speed of lighter particle = -21.53 m/s

Speed of other particle = 3.8 m/s

Explanation:

Let mass of the lighter object be m

Thus mass of heavier object = 4m

Speed of lighter particle = 19 m/s

Speed of second particle with opposite direction = - ⅓(19) m/s = -19/3 m/s

Now, from the formulas of momentum before collision = momentum after collision, and also kinetic energy before collision = Kinetic Energy after collision, we have;

v_bf = [2m_a/(m_a + m_b)]v_ai + [(m_b - m_a)/(m_a + m_b)]v_bi

Now, in this question;

m_a = m

m_b = 4m

v_ai = 19

v_bi = -19/3 m/s

Thus;

v_bf = [2m/(m + 4m)]19 + [(4m - m)/(m + 4m)](-19/3)

Simplifying to get;

v_bf = 19(2m/5m) - (19/3)(3m/5m)

>> v_bf = 38/5 - 19/5

>> v_bf = 19/5 m/s

>> v_bf = 3.8 m/s

Similarly;

v_af = [(m_a - m_b)/(m_a + m_b)]v_ai + [2m_b/(m_a + m_b)]v_bi

v_af = 19((m - 4m)/(m + 4m)) - (19/3)((2 × 4m)/(m + 4m))

This gives;

v_af = 19(-3m/5m) - (19/3)(8m/5m)

v_af = -(57/5) - (152/15)

v_af = -323/15

v_af = -21.53 m/s

The direction in which the 25 kg mass will move is to the Left. The correct option is A.

This is because the force pulling to the left is greater than that to the right.

The velocity of the mass after 1 second will be 0.4 m/s

The velocity of the mass after 2 seconds will be 0.8 m/s

The net force o the mass of 25 kg is given below:

Net force = 20 N - 10 N

Net force = 10 N

The velocity of the mass is given by the formula below:

Velocity = net force * time / mass

velocity after 1 second = 10 * 1 / 25

velocity after 1 second = 0.4 m/s

velocity after 2 seconds = 10 * 2 / 25

velocity after 2 seconds = 0.8 m/s

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Answer:

120

Work :

W = Fd (work = force x distance)

Force :

F = W/d

Distance :

d = W/F

Answer:

69.28 m/s

Explanation:

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

Power = 400 Watt

Time (t) = 10 minutes

Mass (m) = 100 Kg

Velocity (v) =?

Next, we shall convert 10 mins to seconds (s). This can be obtained as follow:

1 min = 60 s

Therefore,

10 mins = 10 × 60

10 mins = 600 s

Next, we shall determine the energy. This can be obtained as follow:

Power = 400 Watt

Time (t) = 600 s

Energy (E) =?

E = Pt

E = 400 × 600

E = 240000 J

Finally, we shall determine how fast the cart is moving. This can be obtained as illustrated below:

Mass (m) = 100 Kg

Energy (E) = Kinetic energy (KE) = 240000 J

Velocity (v) =?

KE = ½mv²

240000 = ½ × 100 × v²

240000 = 50 × v²

Divide both side by 50

v² = 240000 / 50

v² = 4800

Take the square root of both side

v = √4800

v = 69.28 m/s

Thus, the cart is moving with a speed of 69.28 m/s

Answer:

The characteristics that determine how easily two substances change temperature are:

The volume and density of the substances and the amount of time they are in contact do not directly affect how easily they change temperature.

Explanation:

Answer:

67.28 N

Explanation:

Given that,

The mass of an box, m = 15.2 kg

The coefficients of static and kinetic frictions for plastic on wood are 0.55 and 0.36, respectively.

The force of static friction,

\(F_s=\mu_smg\\\\F_s=0.55\times 15.2\times 9.8\\\\F_s=81.92\ N\)

The force of kinetic friction,

\(F_k=\mu_kmg\\\\F_k=0.36\times 15.2\times 9.8\\\\F_k=53.62\ N\)

Net force acting on the object is :

F = 120.9 -53.62

= 67.28 N

Hence, this is the required solution.

Answer:

the moment of inertia is 4.5 × 10⁻⁵ kg.m²  

Explanation:

Given that;

point mass m = 0.005 g = ( 0.005 / 1000 ) = 5 × 10⁻⁶ kg

perpendicular distance r = 3m

We know that a point mass doesn't have a moment of inertia around its own axis but, but using the parallel axis theorem, a moment of inertia around a distant axis of rotation can be determined using;

\(I_{}\) = mr²

so we substitute

\(I_{}\) = (5 × 10⁻⁶ kg) × (3 m)²

\(I_{}\) = (5 × 10⁻⁶ kg) × 9 m²

\(I_{}\)  = 4.5 × 10⁻⁵ kg.m²  

Therefore; the moment of inertia is 4.5 × 10⁻⁵ kg.m²  

The moment of inertia of given point mass is 4.5 × 10⁻⁵ kgm² at a perpendicular distance of 3 m.

The moment of inertia of given point mass can be determined by,

\(I = mr^2\)

Where,

\(I\)- moment of inertia

\(m\)- mass = 0.005 g = ( 0.005 / 1000 ) = 5 × 10⁻⁶ kg

\(r\) - perpendicular distance = 3 m

Put the values in the formula,

\(I = (5 \times 10^{-6}{\rm \ kg}) \times (3 {\rm \ m})^2\\\\I = 5 \times 10^{-6}{\rm \ kg} \times 9 {\rm \ m}\\\\I = 4.5 \times 10^{-5} kgm^2\)

Therefore; the moment of inertia of given point mass is 4.5 × 10⁻⁵ kgm².

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Answer:

1000 L= 1000 kg

1.000 L= 1.000 kg

Explanation:

It will be the same because L and kg have the same mass

A. Wearing appropriate running shoes for your environment is an example of being proactive in your workouts.

There are several ways to become proactive in workouts:

(1) Set specific goals: Setting specific and measurable fitness goals can help you stay focused and motivated. It can also help you track your progress and make necessary adjustments to your workout routine.

(2) Plan your workouts: Planning your workouts ahead of time can help you stay organized and committed to your fitness routine. This can include scheduling your workouts in advance and creating a workout plan that targets your specific goals.

(3) Track your progress: Tracking your progress can help you stay motivated and see how far you've come. This can include keeping a workout journal, taking progress photos, or using a fitness tracker.

(4) Stay consistent: Consistency is key when it comes to achieving fitness goals. Set a regular workout schedule and stick to it as much as possible.

(5) Listen to your body: Pay attention to how your body feels during and after workouts. If something doesn't feel right, make adjustments or seek guidance from a fitness professional.

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Answer:

A.Radio waves

Explanation:

Answer:

6.86 m/s

Explanation:

The minimal velocity needed is when we have only vertical motion, then i will think in the problem only in one axis.

I suppose that the only force, in this case, is the gravitational force acting on the fish.

Then the gravitational equation of the fish will be:

a(t) = -9.8m/s^2

For the velocity equation we need to integrate over time to get:

v(t) = (-9.8m/s^2)*t + v0

Where v0 is the initial velocity of the fish and is what we want to find.

For the position equation we need to integrate over time again to get:

p(t) = (1/2)*(-9.8m/s^2)*t^2 + v0*t + p0

p0 is the initial position of the fish, and because he starts one the water, the initial position is p0 = 0 m

Then the equation is:

p(t) = (1/2)*(-9.8 m /s^2)*t^2 + v0*t

p(t) = (-4.9 m/s^2)*t^2 + v0*t

We know that the maximum height is 2.4m

The value of time at which the fish gets his maximum height is when the velocity of the fish is equal to zero, then we first need to solve:

v(t) = (-9.8m/s^2)*t + v0 = 0

      t = v0/9.8m/s^2

Now we replace this in the position equation to get the maxmimum height, which is equal to 2.4m

2.4m = p( v0/9.8m/s^2) =  (1/2)*(-9.8 m /s^2)*(v0/9.8m/s^2)^2 + v0*(v0/9.8m/s^2)

2.4m = (1/2)(-v0)^2(-9.8 m /s^2) + v0^2/(9.8m/s^2))

2.4m = (1 - 1/2)*v0^2/(9.8m/s^2)

2.4m = 0.5*v0^2/(9.8m/s^2)

2.4m/0.5 = v0^2/(9.8m/s^2)

4.8m*(9.8m/s^2) = v0^2

√(4.8m*(9.8m/s^2)) = v0 = 6.86 m/s