Power Formula: Derivation of Power formula, Examples

We all are very familiar with power. Also, it helps us to measure the energy that we use to do the work. In this topic, we will discuss what is power and what is Power formula, its derivation and solved examples.

Power

Power refers to the quantity of work done by a body. Also, quantity work has to do with a force causing a displacement. Moreover, work has nothing to do with the amount of time, which this force acts to cause the displacement. In addition, there are times when we do work quickly and there are times when we do work rather slowly.

For example, a trail hiker (One who selects an easier path up the mountain) can elevate her/his body a few meters in a short amount of time. On the other hand, a rock climber might take relatively more time to elevate her/his body up a few meters next to the side of a cliff.

Although, both of them do the same work but the rock climber might take more time than the trail hiker. Also, the quantity that has something to do with the rate at which a certain amount of work is done is called power. Besides, in the above case, the hiker has greater power rating than the rock climber.

Power Formula

We can refer to power as the rate at which we do work. Also, it is the ratio of work and time. Besides, we calculate it mathematically using this formula or equation.

Derivation of Power formula

Power = unit of measure (Watt)
W = work done by the body
t = time taken to do the work

Moreover, the standard unit of measuring power is Watt. According to the power formula, a unit of power is equal to a unit of work divided by a unit of time. Also, a watt is equal to Joule/ second.

Besides, due to historical reasons, power is occasionally used to describe the power delivered by a machine. In addition, one horsepower equals 750 Watt.

Suppose that there is a car engine of 40 horsepower that could accelerate from 0 mi/hr to 60 mi/hr in 16 seconds. Moreover, if there is a car that has four times the horsepower that could do the same work in one-fourth the time. That means a 160 horsepower engine could accelerate the car from 0 mi/hr to 60 mi/hr in just 4 seconds.

Here the point is that for some amount of work, power and time are inversely proportional. Moreover, it means that a more powerful engine can do the same work in less time.

Solved Examples on Power Formula

Example 1

Suppose that Mr. X elevates his body of 80 kg up by a 2.0-meter stairwell in 1.8 seconds. Also, in this case, then we could calculate Mr. X power rating. Besides, we must assume that Mr. X must apply an 800 Newton downward force upon the stairs to elevate his body. In addition, by doing this the stairs would push upward on Mr. X body with just enough force to lift his body up the stairs.

Besides, we can assume that the angle between the force of the stairs on Mr. X and Mr. X’s displacement is 0 degrees. Then power can be resolute as shown below:

Solution: Power = Work/Time

W = 871 Watts.

So, Mr.X power rating is 871 Watts.

Example 2

Calculate the power that a person requires to lift an object to a height of 8 m in 10 seconds. Also, the mass of the object is 10 kg. Besides, take g = 10 m/s^2

Solution: For calculating work first find the work done by the person which is equal to the potential energy at that height

Work (W) = mgh = 10 × 8 × 10 = 400J

Power =  Work/Time = 800/10 = 80 J/s.

Formula for Velocity: Concepts, Formulas and Examples

Everybody knows about velocity but there is a misconception about it. The misconception is that speed and velocity are the same things but in reality, it is just the opposite. Besides, most of the people consider them the same and use them interchangeably. Moreover, they are quite similar but they are not same. Besides, in this topic, we will talk about formula for velocity.

Velocity

It refers to the rate of change in displacement with respect to time. Furthermore, distance and displacement are the key points of the velocity. Also, if there is no displacement in objects potion and the object do not cover any distance then there will be no velocity.

Hence, what is the difference between displacement and distance? Displacement refers to the net change in the position of an object in motion. On the other hand, distance refers to the amount of ground covered by an object in motion.

Moreover, distance is a scalar quantity because it can be described with the help of only the magnitude and it has no reference with direction. Whereas, displacement is a vector quantity because it is fully described with both direction and magnitude. In addition, velocity is the function of displacement and is also a vector quantity.

Velocity Formula

Now let’s look at the formula of velocity. As discussed earlier, velocity is a change in objects displacement over time. In simple words, velocity is a measure of how much time an object takes to reach a destination with direction. Moreover, it is directly related to displacement and inversely relates to the time traveled. Also, its unit is meter per second (m/s).

Velocity formula = displacement ÷ time

Displacement = final position – initial position or change in position

Time = taken to cover the distance.

Now let’s take some values to understand the formula clearly. Suppose Mr. X initial position is ai and his final position is af and he has taken t time to cover this distance then the equation will be.

v = af – ai / t = a / t

Here

v = velocity which is m/s (meter per second)

af = final position of X

ai = initial position of X

t = time taken by the object to move along the distance (s)

a =change in position (final – initial) (m)

Solved Example on Velocity Formula

Now let’s test the equation with the help of examples.

Example 1- Suppose there is an object traveled a distance of 10 meters in the left direction and the time taken by the object is 2 minutes. Find the velocity of the object.

Solution

Now recall the formula which is velocity = displacement ÷ time

v = a / t

Now put the values in the formula. But first of all change minutes into time by multiplying minutes by 60.

Time in seconds = time in minutes × number of seconds in a minute

ts = 2 × 60 = 120 s

So, time in seconds is 120 s

v = 10 / 120

v = 0.08 m/s

The velocity of the object is 0.08 m/s.

Example 2- Now let’s discuss another problem where we know the value of velocity and time and we have to calculate displacement. The value of velocity and time is 1.5 m/s and time taken is 100 seconds. Find the value of displacement.

Solution

Now recall the formula which is velocity = displacement ÷ time

v = a / t

Now put the value in the formula

v = a or a / t

1.5 = a ÷ 100

1.5 × 100 = a or

a = 1.5 × 100 = 150 m

The displacement is 150 m.

Density Formula: Meaning, Definition, Solved Examples

Density is a basic and fundamental concept in physics and engineering. Furthermore, it has a strong relationship with the mass of an object. Moreover, this measurement is essential in determining whether something would float or not on a fluid’s surface. Density is certainly one of the most important details you can know about an object. Learn the density formula here.

What is Density?

Density refers to the measurement of the amount of mass of a substance per unit of volume. This measurement of a pure substance has the same value as its mass concentration. Densities vary with different materials or substances. Moreover, this particular measurement of a material can be relevant to purity, buoyancy, and packaging.

One can simplify this measurement’s comparisons across the different systems of units. The replacement of this measurement with a concept is known as relative density can sometimes take place. Relative densities refer to the ratio of a substance’s density to a standard substance or material, usually water.

The densities of materials show variation with pressure and temperature. This variety is comparatively small for solids and liquids but significantly greater when it comes to gases. When the pressure on an object increases, then consequently the volume decreases. This ultimately causes an increase in this particular measurement of the object.

Also, increasing a substance’s temperature results in a decrease in this measurement. This is due to the increase in volume. Heating the bottom of a liquid in most cases results in a decrease in this measurement of such heated liquid.

Density Formula

Densities refer to the measure of relative compactness. The definition of this measure can be expressed as mass, m, in a particular volume, v. Most noteworthy, the symbol ρ is mostly made use of for expressing this measurement. Furthermore, this symbol happens to be the lower case Greek letter rho. Some individuals also make use of the letter D for expressing this measurement.

Solved Example on Density Formula

Q1. Find out the density of a cube of sugar which weighs 12 grams and measures 2 cm on a side?

Answer: This question can be completed in two steps

Step 1: Derive the mass and volume of this sugar cube

Mass = 12 grams

Volume = 2 cm sides

The volume of a cube = (length of side)3

Volume of cube = (length of side)3

Volume = (2)3

Volume = 8 cm3

Step 2: Putting the variables into the formula

Density = mass/volume = 12 grams/8 cm3

So, it comes out to be = 1.5 grams/cm3

Hence, this sugar cube has a density of 1.5 grams/cm3.

Q2. A particular solution of salt water contains 20 grams of salt and 200 grams of water. Find out the density of the salt water? (note = density of water is 1 g/mL)

Answer: Step 1: Derive the mass and volume of the salt water.

Mass of salt = 20 grams

Density of water = mass of water/volume of water

Mass of water = 1 g/mL multiplied by 200 mL

Therefore, the mass of water = 200 grams

Now, one can find out the mass of the saltwater

Mass of salt water = mass salt + mass of water

Mass of salt water = 20 g + 200 g

So, mass of salt water = 220 g

Also, the volume of salt water is 200 mL.

Step 2: Putting these values into the formula

Density = mass/volume = 220 g/200 mL

So, it comes out to be = 1.1 g/mL

Hence, this salt water certainly has a density of 1.1 g/mL.

Acceleration Formula: Definition, Speed, Solved Examples

You must have heard of the term acceleration in your daily life. If we look at it in general, acceleration is said to be when an object is increasing its speed cautiously. In other words, it means if you are traveling in a car which is moving at the speed of 60 kmph and after 1 min the speed of the car is 65 kmph, which means you are accelerating. Now the question arises that how can you say that this object is accelerating? What are the terms taken into consideration during the calculation of acceleration? We will dive deeper below and learn the acceleration formula.

Acceleration Formula | Definition

In general, we can say acceleration refers to speeding up. However, from the physics perspective, we see it means something different. Over here, it is referred to as the rate at which the velocity of an object changes. It does not matter if it is speeding up or down, it’s the change.

Therefore, the acceleration is positive when the object is speeding up and negative when speeding down. According to Newton’s Second Law, the net unbalanced force which acts on the object causes this to happen. Thus, it can be said that acceleration is a vector quantity. It is so because it changes the time rate of change of velocity.

Formula for Acceleration

There are two formulas for acceleration. The first formula is from Newton’s second law relates force, mass, and acceleration in an equation. Thus, the formula is:

F= ma

Over here:

F refers to the force

m is the mass

a is the acceleration

Further, we have another formula that is made to calculate the rate of change in velocity over the period of time. Therefore, the formula for this is:

Solved Examples on Acccerelation Formula

Question- A woman is traveling by her sports car at a constant velocity v = 5.00 m/s. When she steps on the gas, it makes the car to accelerate forward. Further, past 10.0 seconds, she stops the acceleration and continues a constant velocity v = 25.0 m/s. Calculate the acceleration of the car.

Answer- In the forward direction, initial velocity is

Therefore, we see that the acceleration of the car is 2.00 m/sforward.

Question- A man takes a rock and drops it off from a cliff. It falls for 15.0 s before it hits the ground. The acceleration due to gravity g = 9.80 m/s2. Calculate the velocity of the rock the moment before it had hit the ground.

Answer- The man released the rock from rest, therefore, we get the initial velocity as

$V_{i}$

= 0.00 m/s. The time for the change to take place is 15.0 s. The acceleration for this is 9.80 m/s2. Therefore, to find the velocity we will rearrange the equation like:

Therefore, as the rock is falling, the direction of the velocity is down.

Pendulum Formula: Definition, Pendulum Equation, Examples

A pendulum is one of the most common items found in most households. It is a device that is commonly found in wall clocks. This article will throw light on this particular device and its functioning. After that, students will be able to easily understand how it operates and the reason behind its harmonic motion. Learn pendulum formula here.

Pendulum Definition

A pendulum is essentially a weight that is hung from a fixed point. It is placed in such a way that it allows the device to swing freely to and fro. The pendulum bob of a simple pendulum is treated as a point mass. Further, the string from which it’s hanging is of negligible mass.

If you look at it from the perspective of physics, you will find these simple pendulums quite intriguing. This is so because they serve as a great example of simple harmonic motion, which is much similar to rubber bands or springs.

Pendulum Equation

There are a lot of equations that we can use for describing a pendulum. Firstly, we have the period equation which helps us calculate how long the pendulum takes to swing back and forth. We measure it in seconds. Thus the period equation is:

T = 2π√(L/g)

Over here:

T= Period in seconds

π= The Greek letter Pi which is almost 3.14

√= The square root of which we include in the parentheses

L= The length of the rod or wire in meters or feet

G= The acceleration due to gravity (9.8 m/s² on Earth)

Next up, we have the frequency equation. This calculates the numbers of times a pendulum swings back and forth within a second. We measure that in hertz. Thus, the frequency equation is:

f = 1/T

f = 1/[2π√(L/g)]

Over here:

Frequency f is the reciprocal of the period T:

Further, we have the length of the wire. You can easily find the length of the wire or rod for a specified frequency or period. Have a look at the equation given below to know more:

f = [√(g/L)]/2π

2πf = √(g/L)

So, when you have this, you will need to square both sides of these equations. That results in:

4π2f2 = g/L

When you solve for L, you will get:

L = g/(4π2f2)

Similarly, the length of the wire for a given period is:

T = 2π√(L/g)

Then, you after squaring both the sides we get:

T2 = 4π2(L/g)

Thus, when you will solve for L, you will get:

L = gT2/4π2

Solved Example on Pendulum Formula

Question– A pendulum’s length is 4 meters. It completes one full cycle of 0.25 times every second. The maximum displacement that the pendulum bob reaches is 0.1 meters from the center. Find out the time period of the oscillation? And what is the displacement after 0.6 seconds?

Answer– To begin with, make sure to write down the information which you already know. So, by far, we already know the length of the pendulum (L= 4 meters). Then, the pendulum’s frequency is 0.25 (f- 0.25). Similarly, the amplitude or maximum displacement is 0.1 and time is 0.6 (A= 0.1 and t=0.6). Finally, the acceleration due to gravity, as always is 9.8 (g=9.8). So, you need to find T.

In order to find T, you need to simply plug numbers into this equation and solve it accordingly. So, you have the equation of 2π times the square root of 4 which you will divide by 9.8. Thus, the equation will be:

2π × 0.64

2 × 3.14 × 0.64 = 4.01

Therefore, the time period of the oscillation is 4.01 seconds.

Physics Formulas

Physics Formulas can be sometimes difficult to remember. It’s good idea to have a cheat sheet of Physics formulas always with you. So, we have created awesome list of formulas of physics. The following list contains all the formulas from CBSE Class 5 to Class 12. These formulas are the most used expressions, equations, rules, statements in Physics. From Acceleration formula to Magnetism formula. We have covered everything just for you.

List of Physics Formulas

• Pendulum Formula
• Acceleration Formula
• Density Formula
• Velocity Formula
• Power Formula
• Reynolds Number Formula
• Kinetic Energy Formula
• Fahrenheit to Celsius Formula
• Force Formula
• Momentum Formula
• Work formula
• Potential Energy Formula
• Pressure Formula
• Torque Formula
• Wave Formula
• Average Speed Formula
• Frequency Formula
• Half Line Formula
• Mass Formula
• Unit Vector Formula
• Angular Velocity Formula
• Cylinder Formula
• Displacement Formula
• Horizontal Range Formula
• Moment of Inertia Formula
• Thermal Energy Formula
• Angular Momentum Formula
• Average Velocity Formula
• Capacitance Formula
• Cone Formula
• Impulse Formula
• Resistance Formula
• Weight Formula
• Centripetal Force Formula
• Coulombs Law Formula
• Efficiency Formula
• Gravity Formula
• Kirchhoffs Junction Rule Formula
• Specific Gravity Formula
• Specific Heat Formula
• Trajectory Formula
• Distance Formula Physics
• Angular Acceleration Formula
• Centripetal Acceleration Formula
• Cross Product Formula
• Electric Field Formula
• Electric Power Formula
• Inductance Formula
• Kirchhoffs Loop Rule Formula
• Newton’s Law of Cooling Formula
• Refractive Index Formula
• Resistivity Formula
• Stress Formula
• Time Dilation Formula
• Wavelength Formula
• Electric Potential Formula
• Electrical Formulas
• Entropy Formula
• Flow Rate Formula
• Gravitational Force Formula
• Gravitational Potential Energy Formula
• Kinematics Formulas
• Magnetic Field Strength Formula
• Speed Distance Time Formula
• Strain Formula
• Surface Tension Formula
• Angular Speed Formula
• Average Acceleration Formula
• Brewsters Law
• Continuous Compound Interest Formula
• Escape Velocity Formula
• Friction Force Formula
• Friction Formula
• Heat Capacity Formula
• Magnetic Field Formula
• Resistors in Series Formula
• Voltage Drop Formula
• Amplitude Formula
• Centroid Formula
• Doppler Effect Formula
• Elastic Formula
• Heat Formula
• Ideal Gas Law Formulas
• Speed of Sound Formula
• Spring Constant Formula
• Temperature Formula
• Transformer Formula
• Wave Speed Formula
• Work Formula Physics
• Basic Physics formulas
• Beam Deflection Formula
• Buoyancy Formula
• Celsius to Kelvin Formula
• Center of Mass Formula
• Electric Current Formula
• Electrical Resistance Formula
• Instantaneous Velocity Formula
• Internal Energy Formula
• Mechanical Energy Formula
• Moment Formula
• Time of Flight Formula
• Voltage Divider Formula
• Youngs Modulus Formula
• Angular Frequency Formula
• Bulk Modulus Formula
• Critical angle Formula
• Current Density Formula
• Elastic Potential Energy Formula
• Free Fall Formula
• Horsepower Formula
• Inelastic Collision Formula
• Initial Velocity Formula
• Kelvin to Celsius Formula
• Latent Heat formula
• Net Force Formula
• Speed Formula Physics
• Stopping Distance Formula
• Thermal Conductivity Formula
• Wavelength Frequency Formula
• Acceleration due to Gravity Formula
• Air Resistance Formula
• Capacitors in Parallel Formula
• Celsius Formula
• Combustion Formula
• Conservation of Energy Formula
• Deceleration Formula
• Electricity Formulas
• Intensity Formula
• Normal Force Formula
• Resonant Frequency Formula
• Resultant Force Formula
• Time Formula Physics
• Displacement Formula Physics
• Capacitive Reactance Formula
• De Broglie Wavelength Formula
• Drag Force Formula
• Electric Flux Formula
• Energy Formula Physics
• Heat Transfer Formula
• Instantaneous Rate of Change Formula
• Kinetic Friction Formula
• Linear Momentum Formula
• Linear Speed Formula
• Magnetic Force Formula
• Mass Flow Rate Formula
• Measurement Formulas
• Molar Concentration Formula
• Resistors in Parallel Formula
• Rotational Inertia Formula
• Rydberg Formula
• Shear Modulus Formula
• Simple Harmonic Motion Formula
• Static Friction Formula
• Tangential Acceleration Formula
• Thermal Expansion Formula
• Uniform Circular Motion Formula
• Ohms Law Formula
• Absolute Pressure Formula
• Angular Displacement Formula
• Decibel Formula
• Gram Formula Mass
• Heisenberg Uncertainty Principle Formula
• Inductive Reactance Formula
• Inverse Square Law Formula
• Orbital Velocity Formula
• Relative Velocity Formula
• Sound Intensity Formula
• Terminal Velocity Formula
• Average Force Formula
• Capacitors in Series Formula
• Charge Density Formula
• Diffraction Grating Formula
• Drag Formula
• Dynamic Viscosity Formula
• Energy Density Formula
• Heat of Vaporization Formula
• Kinematic Viscosity Formula
• Mach Number Formula
• Maximum Height Formula
• Strain Energy Formula
• Tension Formula
• Volume Flow Rate Formula
• Water Pressure Formula
• Archimedes Principle Formula
• Distance Traveled Formula
•  Acceleration Formula
• Instantaneous Speed Formula
• Lattice Energy Formula
• Rotational Kinetic Energy Formula
• Velocity Formula Physics
• Calorimetry Formula
• Electric resistance Formula
• EMF Formula
• Equivalent Resistance Formula
• Fluid Mechanics Formula
• Friction Loss Formula
• Lens Makers Formula
• Linear acceleration Formula
• Magnetism Formula
• Orbital Speed Formula
• Physics Motion Formulas
• Spring Force Formula
• Surface Charge Density Formula
• Angle between Two Vectors Formula
• Beat Frequency Formula
• Coefficient of Static Friction Formula
• Doppler Shift Formula
• Heat Index Formula
• Heat Loss Formula
• Heat of Fusion Formula
• Latent Heat of Fusion Formula
• Position Formula
• Pressure Drop Formula
• Tangential Velocity Formula
• Gauss Law Formula
• Gravitational Field Formula
• Gravity Formula Physics
• Heat Flux Formula
• Heat Input Formula
• Heat of Reaction formula
• Length Contraction Formula
• Planetary Formulas
• Refraction Formula
• Relativity Formula
• Spring potential energy Formula
• Uncertainty Principle Formula
• Energy of a wave Formula
• DC Voltage Drop Formula
• Momentum Of Photon Formula
• Optics Formula
• Parallel Axis Theorem Formula
• Photoelectric Effect Formula
• Physics Kinematics Formulas
• Universal Gravitation Formula
• Waves Physics Formulas
• Wheatstone Bridge Formula