prove: st = ut+½ at²​

Answer:

The position of the image = 7.2 cm.

Explanation:

Given:

A Converging lens:

Object distance [tex](d_o)[/tex] = 12 cm = -12 cm (sign convention)

Focal length [tex](f)[/tex] = 18 cm

We have to find the position of the image.

Let the position of the image be [tex](d_i)[/tex] .

Sign convention:

The focal length of converging (convex) lens is always positive,while object distance is negative.

Using lens formula:

⇒ [tex]\frac{1}{object\ distance} + \frac{1}{image\ distance} =\frac{1}{focal\ length}[/tex]

⇒ [tex]\frac{1}{d_o} + \frac{1}{d_i} = \frac{1}{f}[/tex]

⇒ [tex]\frac{1}{d_i} =\frac{1}{f} - \frac{1}{d_o}[/tex]

⇒ [tex]\frac{1}{d_i} =\frac{1}{f} - \frac{1}{-d_o}[/tex]

⇒ [tex]\frac{1}{d_i} =\frac{1}{f} + \frac{1}{d_o}[/tex]

⇒ [tex]d_i=\frac{d_o\times f}{d_o+f}[/tex]

⇒  [tex]d_i=\frac{12\times 18}{12+18}[/tex]

⇒ [tex]d_i=\frac{216}{30}[/tex]

⇒ [tex]d_i=7.2[/tex] cm

So the position of the image = 7.2 cm.

Final answer:

The net force is the greatest when the forces are in the same direction and have the greatest magnitude. The net force is zero when the forces are balanced and cancel each other out.

Explanation:

The net force on an object is the vector sum of all the forces acting on it. The magnitude of the net force can be determined by considering the individual forces acting on the object. The net force is the greatest at points where the forces acting on the object are in the same direction and have the greatest magnitude.

The net force is zero when the forces acting on the object are balanced and cancel each other out. This occurs at points where the forces are equal in magnitude and opposite in direction.

For example, let's say we have two forces acting on an object: 10 N to the right and 5 N to the left. At the point where the forces are added, the net force would be 5 N to the right (10 N - 5 N). This is the greatest net force. At the point where the forces cancel each other out, the net force would be zero (10 N - 10 N).

Answer:

a. 137.5 m

b. 550 m

Explanation:

Accelerated Motion

If an object is changing its velocity at a constant rate, it has a uniformly accelerated motion. When the object is moving in one fixed axis, then the sign of the acceleration is negative if the object is braking, and positive if the object is increasing its speed.

The initial speed vo, final speed vt, acceleration a, and distance traveled x are related by the formula

[tex]v_f^2=v_o^2+2ax[/tex]

a. The Race Car A has an initial speed of 55 m/s and it's said to stop. We must find at what distance it goes to vf=0. This means that the above formula becomes

[tex]0=v_o^2+2ax[/tex]

Solving for x

[tex]\displaystyle x=-\frac{v_o^2}{2a}[/tex]

The acceleration is [tex]-11\ m/s^2[/tex], negative because it's against the movement. Thus

[tex]\displaystyle x=-\frac{55^2}{2\times (-11)}[/tex]

[tex]x=137.5\ m[/tex]

b. If the car is going twice as fast (v0=110 m/s), then  

[tex]\displaystyle x=-\frac{110^2}{2\times (-11)}[/tex]

[tex]x=550\ m[/tex]

Answer:

Pound

Explanation:

SI Unit stands for the International Standard of Unit. Thus from the options given, metre is a measure of length which is an SI unit. Kilogram is a measure of mass of a goven matter which is also an SI unit. Second is a measure of time which is an SI unit. Pound is a measure of masswhich is not an SI unit  but has to be converted to kilograms which an SI unit.

The pound is not an SI unit, while the kilogram, meter, and nanometer are part of the International System of Units (SI).

The SI (International System of Units) is a globally recognized system of measurement that includes specific base units, derived units, and prefixes for expressing measurements consistently. It was developed to standardize measurements worldwide. Let's identify which of the options is not an SI unit:

Kilogram (kg): The kilogram is one of the seven base SI units and is the unit of mass. It is used to measure the amount of matter in an object. The symbol for the kilogram is "kg."

Meter (m): The meter is another base SI unit and is the unit of length. It is used to measure distance or length. The symbol for the meter is "m."

Nanometer (nm): The nanometer is not a base SI unit, but it is an SI-accepted metric prefix. It represents one billionth (1/1,000,000,000) of a meter (10^-9 meters). It is used for very small lengths, particularly in fields like nanotechnology.

Pound: The pound is not an SI unit. It is a unit of mass commonly used in the United States and a few other countries that have not fully adopted the SI system. The pound is equivalent to approximately 0.453592 kilograms.

So, among the given options, the pound is the unit that is not an SI unit. The other three options (kg, meter, nanometer) are all related to the SI system. The SI system promotes consistency and clarity in scientific measurements and is widely used in most countries around the world.

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The question probable may be:

Which of the following is not an SI unit?

kg , pound, meter, nanometer

Answer:

1.857 Ohms

Explanation:

The marked voltage of the battery is it's E.M.F. (Electromotive force). It is the maximum voltage the battery can supply because, ideally internal resistance of a cell or battery should be zero. Let us denote the E.M.F. as E.

In reality we get a lower voltage called the Terminal Voltage (Voltage across the terminals of the battery). Let us call that V. This is due to the voltage drop caused by the internal resistance (say 'r').

So when the circuit is connected a current I flows through a resistance

R(= 5 ohms, given).

Now, potential difference = Terminal Voltage = V = 8.75 Volts

Hence, [tex]I=\frac{V}{R} =\frac{8.75}{5}=1.75 Amperes[/tex]

Now, by conservation of energy we can say that,

E.M.F. = Terminal Voltage + Voltage drop due to the battery's internal resistance

or, [tex]E=V+Ir[/tex]

or, [tex]r=\frac{E-V}{I}=\frac{12-8.75}{1.75}=1.857[/tex] Ohms

Answer:

The definitions of mass, energy, time and space as used in Physics are circular

The Conservation of Mass and Energy

The definition of zero is not sufficiently defined in Physics

Newton’s Laws of Motion are related by Calculus

Knowing the terms of Physics is most important.

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Answer:

Workdone = 12.2 Joules

Explanation:

Given:

Force applied on the pencil = 47 N

Displacement of the pencil = 0.26 m

We have to find the work done .

Note:

Workdone = Product of force and its displacement (in the direction of the force) .

So,

Plugging the values.

Workdone = [tex]Force\times displacement[/tex]

⇒ [tex]W=F\times d[/tex]

⇒ [tex]W =47\times 0.26[/tex]

⇒ [tex]W=12.2[/tex] Joules (J)

OR

We can say that the displacement is against the direction of applied force.

Displacement = - 0.26

Workdone = [tex]F\times d\times cos(\theta)[/tex]

⇒ [tex]\theta[/tex] is the angle between force and displacement.

⇒ Here, [tex]\theta=180[/tex]

⇒ [tex]cos(180) = -1[/tex]

Workdone (W)  = [tex]Fdcos(\theta)[/tex]

⇒ [tex]47\times -0.26\times -1[/tex]

⇒ [tex]12.2[/tex]  Joules (J).

Workdone on pushing the pencil = 12.2 Joules.

Work is the product of the force and displacement. The work done by in the given situation 12.2 J.

Work:

It is the change in the energy due displacement  of the object by the applied force. Work is the product of the force and displacement.

W = f.d

Where,

W - work

f- force =  47 N

d - displacement = 0.26 m.

put the values in the formula,

W =  47 N x 0.26 m.

W = 12.2 J

Therefore, the work done by in the given situation 12.2 J.

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Answer:

40 N/m

Explanation:

The diagram attached is used to answer the question

We know from Hooke's law that extension is directly proportional to the applied force hence

F=kx where x is extension, F is applied force and k is the spring constant. Making k the subject of the formula then

[tex]k=\frac {F}{k}[/tex]

From the attached diagram extension is given by subtracting unstretched spring from stretched spring hence extension, x=1-0.5=0.5m

Substituting 20 N for F and 0.5 m for x then

[tex]k=\frac {20}{0.5}=40 N/m[/tex]

Answer:

1. (F) Increasing the frequency variable reduces the time required.

2. (I) Intensity variable can be related the the energy expended.

3.(T) Time variable would affect the speed.

Explanation:

1. (F) increasing the frequency variable implies that the distance would be covered in lesser time. As a wave of 250Hz cover more distance than that of 200Hz.

2. (I) Intensity variable. An increase in this variable implies that more energy is expended.

3.(T) Time variable can either give the required out come or not. As increasing the time would mean that the speed has reduced, while decreasing the time means the distance would be covered quickly. If the required speed is 20m/s, then increasing it to 30m/s imples that lesser time would be recorded. If the reverse is the case, then more time would be recorded. time = distance/speed

1. reduces the time required.

2.energy expended.

3.affect the speed.

Frequency, time period and intensity are quantitative dimensions which describe the amount of physical activity taking place during a given time.

1. (F) frequency variable - Frequency refers to the number of waves that pass a fixed point in unit time.

i.e. [tex]F =\frac{1}{T}[/tex]

When frequency is increased then distance would be covered in lesser time.

For example, a wave of 550Hz cover more distance than that of 500Hz.

2. (I) Intensity variable-  The quantity of energy the wave conveys per unit time across a surface of unit area.

i.e. [tex]I = \frac{P}{4\pi r^{2} }[/tex]

When Intensity increases it implies that more energy is expended.

3.(T) Time variable -It is define as the ratio of distance and time.

i.e. [tex]time = \frac{distance}{speed}[/tex]

When time variable is increased than  the quantity of energy the wave conveys per unit time across a surface of unit area, speed is reduced.

When time variable is decreased  the distance would be covered quickly.

For example : If the speed  of car is 80m/s, then by increasing the speed  to 100m/s shows that lesser time would be required.

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Answer:

Pressure applied by the man= 285103.125 [tex]Pa[/tex]  or 41.35 [tex]lb/in^{2}[/tex]

Explanation:

Pressure is defined as the perpendicular force applied per unit area.

i.e.  [tex]Pressure=\frac{Force}{Area}[/tex]

Now, [tex]Force= mg[/tex]

where, [tex]m[/tex] = mass of the body(man) = 93 kg

[tex]g[/tex] = acceleration due to gravity of Earth = 9.81 [tex]m/{s^{2}}[/tex]

[tex]Area[/tex] covered is equal to the area of both stilts(a man generally stands on two feet)

therefore [tex]Area=2(0.04)^{2}[/tex] [tex]m^{2}[/tex]

and putting in the values, we get,

[tex]Pressure=\frac{93\times9.81}{2\times(0.04)^{2}}Nm^{-2}=285103.125Nm^{-2}[/tex]

Now we need to convert to our required units:

[tex]1Nm^{-2}=1Pa\\1Pa=0.000145038lb/in^{2}[/tex]

(We can get the above result by individually converting kg to lb and meters to inches respectively)

Using the above relations we get,

[tex]Pressure=285103.125Pa=0.000145038\times285103.125lb/in^{2}=41.35lb/in^{2}[/tex]

Based on the formula for pressure, the pressure applied on the ground is 570206.25 N/m² or 82.7 pound per square inch

Pressure is defined as the perpendicular force applied per unit area.

Also,

where,

mass of the body = 93 kg

g = 9.81 m/s²

Force = 93 * 9,81

Force = 912.33 N

Area of square stilt = (0.04m)²

Area = 1.6 * 10⁻³ m²

Then;

Pressure = 912.33 N/1.6 * 10⁻³ m²

Pressure = 570206.25 N/m²

Converting to pounds per square inch:

1 pound per square inch = 6894.76 N/m²

570206.25 N/m² = 570206.25 N/m² * 1 pound per square inch/6894.76 N/m²

Pressure = 82.7 pound per square inch

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Answer:

With an increase in temperature, there is typically an increase in the molecular interchange as molecules move faster in higher temperatures. The gas viscosity will increase with temperature. ... With high temperatures, viscosity increases in gases and decreases in liquids, the drag force will do the same.

Answer:18m west

Explanation:

Since they are moving in opposite direction we subtract to get the displacement

Displacement =38-20

Displacement =18m in west direction

Explanation:

Work equals the force times the parallel distance.

a) Force gravity is in the downward direction.  The box is moving on flat ground, so there's no displacement in that direction.

W = Fd

W = (50 kg) (-9.8 m/s²) (0 m)

W = 0 J

b) This time, there is a displacement in the vertical direction.

W = Fd

W = (50 kg) (-9.8 m/s²) (5.00 m sin 15.0°)

W = -634 J

c) The force is parallel to the displacement.

W = Fd

W = (100. N) (5.00 m)

W = 500. J

d) Again, the force is parallel to the displacement.

W = Fd

W = (100. N) (5.00 m)

W = 500. J

Answer:

a)Kicking a ball; b) A car that gets hit

Explanation:

a)

A classic example is when a soccer player kicks a moving ball in another direction by modifying the original direction and speed that the ball brought.

b)

Another example is when a car goes on a highway and suddenly is hit by another car on its side modifying the original direction and speed.

Complete Question:

A fully loaded Saturn V rocket has a mass of 2.92 x 106 kg. Its engines have a thrust of 3.34 x 107 N. (8 marks)

a) What is the downward force of gravity on the rocket at blast-off?

b) What is the unbalanced force on the rocket at blast-off?

c) What is the acceleration of the rocket as it leaves the launching pad?

d) As the rocket travels upwards, the engine thrust remains constant, but the mass of the rocket decreases. Why?

e) Does the acceleration of the rocket increase, decrease, or remain the same as the engines continue to fire?

Answer:

a) [tex]-2.8616 \times 10^{7} N[/tex] is the downward force of gravity on the rocket at blast-off.

b) [tex]4.784 \times 10^{6} N[/tex] is the unbalanced force on the rocket at blast-off

c) [tex]1.638 \mathrm{m} / \mathrm{s}^{2}[/tex] is the acceleration of the rocket as it leaves the launching pad

d) Because the propellant here is burned up, hence the mass of the rocket seems to be varied (total mass of all its parts). Thereby, the mass decreases when the rocket moves upward.

e) The acceleration of the rocket increases when engines continue to fire

Explanation:

Given:

Mass (m) =  [tex]2.92 \times 10^{6} \mathrm{kg}[/tex]

a) In physics, weight can be defined as the applied force on a body by gravity. It is the product of mass (m) and gravity [tex]\left(g=9.8 \mathrm{m} / \mathrm{s}^{2}\right)[/tex]

  [tex]\text { weight }(W)=m \times g=2.92 \times 10^{6} \times(-9.8)=28.616 \times 10^{6}=-2.8616 \times 10^{7} N[/tex]

The negative sign indicates the downward force of gravity.

b) To find the unbalanced force on the rocket at blast-off,

Accelerating force,

   [tex]F_{a}=F+W=3.34 \times 10^{7}+\left(-2.8616 \times 10^{7}\right)=(3.34-2.8616) \times 10^{7}[/tex]

   [tex]F_{a}=0.4784 \times 10^{7}=4.784 \times 10^{6} N[/tex]

c) Newton’s second law of motion states that the object’s acceleration depends on two variable:

The equation can be given as below,

    [tex]Force =m \times acceleration[/tex]

    [tex]\text { Acceleration }=\frac{F_{a}}{m}=\frac{4.784 \times 10^{6}}{2.92 \times 10^{6}}=1.638 \mathrm{m} / \mathrm{s}^{2}[/tex]

d) The pushing of rocket upward will happen as long as the engine gets fired. The propellant here is burned up, hence the mass of the rocket seems to be varied (total mass of all its parts). Thereby, the mass decreases (taotal mass) when the rocket moves upward.

e) The acceleration of the rocket increases when engines continue to fire

Let consider [tex]F_{a}[/tex] is constant, mass gets decreasing, then the acceleration would be increasing (as mass and acceleration are inversely proportionate to each other) .

Answer: 258.3 s

Explanation:

The speed [tex]s[/tex] is given by the following equation:

[tex]s=\frac{D}{t}[/tex]

Where:

[tex]s=3(10)^{8} m/s[/tex] is the speed of light in vacuum

[tex]D=2(38776106 km \frac{1000 m}{1 km})=7.75(10)^{10} m[/tex] is the double of the distance between Earth and Moon, since the beam of light travels from Earth to the Moon and back to Earth again.

[tex]t[/tex] is the time it takes to the beam of light to travel the mentioned distance

Isolating [tex]t[/tex] and solving with the given information:

[tex]t=\frac{D}{s}[/tex]

[tex]t=\frac{7.75(10)^{10} m}{3(10)^{8} m/s}[/tex]

Finally:

[tex]t=258.3 s \approx 258 s[/tex]

Answer:

Simple machine

Explanation:

It is a simple machine because the person wants to raise the load by an inclined plane. Simple machines perform work with the mechanical advantage offered by the machine itself, such as using a bar as Lever, lifting a load by means of a pulley. simple machines multiply or change direction a force. While Composite machines are the Union of several simple machines that perform a given job, examples of combined machines are found on bicycles, a washing machine, a car, and others.

Answer:

b

Explanation:

took test, other answer said b and was verified

Answer:

1). the sun at the center, with the earth and other planets orbiting the sun.

Explanation:

Newton believes that it's gravity between the sun and the other planets even at the large distances that cause them to orbit around the sun. This force build up by the masses of the sun and the planets which keeps the planets in their orbit.

Answer:the sun at the center, with the earth and other planets orbiting the sun.

Explanation:

The end voltage is 9.01 volts.

The emf of the battery is 12 volts.

The resistance of the circuit = 1.75 ohms.

The resistance of the applicant attached = 5.5 ohms.

So, total resistance of the circuit = [tex]1.75 + 5.5[/tex] ohms = 7.25 ohms.

According to the equation, the voltage applied is equal to the product of the current and the resistance.

V=iR.

So, 12 = [tex]i \times7.25[/tex].

So, i = 1.66.

Therefore, the voltage at the end of the circuit = [tex]12 - 1.66\times1.75[/tex]volts

= 9.01volts.

So the end voltage is 9.01 volts.

Answer:450joules

Explanation:

Let mass=m velocity =v

Mass given=10g=(10/1000)kg=0.01kg

Velocity given =300m/s

Kinetic energy =(m x v^2)/2

Kinetic energy =(0.01x300^2)/2

Kinetic energy =(0.01 x 90000)/2

Kinetic energy =900/2

Kinetic energy =450joules

Answer:

in a device, an electrical circuit of lower resistance than that of a normal circuit, typically resulting from the unintended contact of components and consequent accidental diversion of the current.

Explanation:

Answer: A short circuit is simply a low resistance connection between the two conductors supplying electrical power to any circuit. This results in excessive current flow in the power source through the 'short,' and may even cause the power source to be destroyed.

Explanation:

Answer:

The energy of the wave will increase by a factor of 1.21.

Explanation:

Given:

The amplitude of the ocean wave is increased by a factor of 1.1.

The energy associated with a wave depends on the amplitude of the wave.

The energy (E) is directly proportional to the square of the amplitude (A) of the wave and is expressed as:

[tex]E=kA^2\\Where\ k\to constant\ of\ proportionality[/tex]

So, if the amplitude is doubled, then the energy will become 4 times and if the amplitude is halved, then the energy reduced by a factor of one by four.

Here, the amplitude is increased by a factor of 1.1. So, the energy associated with it will increase by a factor of square of 1.1 which is given as:

[tex]Increase\ in\ Energy=(1.1)^2=1.21\ of\ the\ initial\ value[/tex]

Therefore, the energy of the wave will increase by a factor of 1.21.

Answer:

(a) -0.636 m/s²

(b) -19.08 N

Explanation:

Given:

Mass of the rocket (m) = 30.0 kg

Initial velocity of rocket (v) = 5.00 m/s

Initial time of rocket (t₁) = 3.00 s

Final velocity of the rocket (u) = -2.00 m/s

Final time of rocket (t₂) = 14.0 s

(a)

Acceleration is given as the rate of change of velocity. Therefore,

[tex]a=\frac{u-v}{t_2-t_1}\\\\a=\frac{-2.00-5.00}{14.00-3.00}\ m/s^2\\\\a=\frac{-7.00}{11.00}\ m/s^2\\\\a=-0.636\ m/s^2[/tex]

Therefore, the acceleration of the rocket is 0.636 m/s².

(b)

From Newton's second law, we know that, force acting on a body is equal to the product of its mass and acceleration.

So, the force acting on the rocket is given as:

[tex]F=ma\\\\F=(30.0\ kg)(-0.636\ m/s^2)\\\\F=-19.08\ N[/tex]

Therefore, the force acting on the rocket is -19.08 N.

The negative sign implies the force acts in the direction opposite to motion.

Answer: The temperature of the air affects the speed of sound in the due to the fact that colder contains air molecules with low kinetic energy. For warm air the kinetic energy of the molecules is high causing them to move in rapid motion. Because of these vibrations and collisions sound waves moves in a faster rate.

Explanation:

Answer: Fnet = 40 N on the right

Explanation: The net force is the summation of forces acting on an object. Add the forces in the same direction and subtract to the opposing force moving in the opposite side.

Fnet= F1 + F2 - F3

= 120 N + 60 N - 140 N

= 180 N - 140 N

= 40 N on the right

Explanation:

[tex] \frac{1}{12} + \frac{7}{9} \\ \\ = \frac{1 \times 3}{12 \times 3} + \frac{7 \times 4}{9 \times 4} \\ \\ = \frac{3}{36} + \frac{28}{36} \\ \\ = \frac{3 + 28}{36} \\ \\ = \frac{31}{36} \\ \\ \huge \purple{ \boxed{\therefore \: \frac{1}{12} + \frac{7}{9} = \frac{31}{36} }} \\ [/tex]

Answer:

31/36

Explanation:

do the math you will see

Answer:

40 N/m

Explanation:

Assuming that the missing diagram is as attached, then we can deduce from Hooke's law that the extension of a spring is directly proportional to the applied force. This is mathematically expressed as

F=kx

Here, F represent the applied force, x denote the extension of the spring while k is the spring constant.

From the attached diagram, extension of the spring x=1-0.5=0.5m

Substituting 20 N for F and 0.5 m for x then

20=0.5k

k=20/0.5=40 N/m

Answer:

pure constructive interference

Explanation:

The crests of two waves and the troughs are aligned. The superposition produces pure constructive interference. Because the disturbances add pure constructive interference, it produces a wave that has twice the amplitude of the individual waves but has the same wavelength.

Newton's first law says the cart should keep going if there's no force acting on it to slow it down. But it slows down and stops. Is there any force acting on it ? You bet ! There's friction in the wheels, and a little bit of air resistance too.

Answer:

120J

Explanation:

Work done = Force (N) X Distance (m)

Answer:

Work = 120Nm or 120J

Explanation:

Work is said to be done when a force moves a body over a distance, in the direction of force applied.

Work done = force x distance (in the direction of the force)

Therefore work = force x displacement

As displacement is distance in a specific or specified direction.

From the parameters given

Force = 30N

Displacement = 4m.

Therefore work = force x displacement

                         = 30N x 4m

Work = 120Nm or 120J

Note :J is joules which is the S. I unit of work

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