What is the relation between power and velocity

Energy can be converted between different forms.

Let’s start with a different example though, to understand the relation between power and energy.

Distance and velocity.

Distance is described in units of meters and velocity is described in units of meters per second.

So the difference between distance and velocity is that velocity is divided by time.

With power and energy, power is units of energy divided by time. The same difference as distance and velocity.

The units of power are watts, the units of energy are joules. A watt is one joule divided by one second.

FAQ

What is the difference between energy and power?

-Power is energy divided by time. Often units of J/s (joules/second).

When calculating the amount of electrical energy, you multiply electrical power times what?

-You multiply the power by the time (be aware of the right units for the situation) to get energy

What are the differences between energy and electricity?

-There are many types of energy, the electrical energy from an electric potential is one type of energy.

What does power measure?

-Power measures energy per time. So joules per second is one expression of power. A kilowatt is 1,000 watts.

What is the equation to calculate power?

-That depends on the situation.

What is the difference between watts and kilowatts?

-A kilowatt is 1,000 watts, much like a kilometer is 1,000 meters.

What is the relationship between power and energy and time?

-If you multiply power by time, you get energy. If you divide energy by time, you get power.

P = E/t

You can rearrange that equation in a few ways.

Answer

Verified

Hint This is quite an easy question. We can directly get the answer by substituting the given values. To show that power= force* velocity, we know the formula for power, substitute the work done formula in power formula and use that same derivation to find the power of the given body.

Complete step by step answer

Power is the rate of doing work. It is the energy or strength of a body. Power is given by the ratio of work done by time. The unit of power is Watt (W).$ \Rightarrow P = \dfrac{W}{t}{\text{ }} \to {\text{1}}$P is the powerW is the work done Work done is the product of force and displacement. $ \Rightarrow W = F \times d$F is forced is distance travelled or displacementThen power can be written as$ \Rightarrow P = \dfrac{{F \times d}}{t}$$ \Rightarrow P = F \times \dfrac{d}{t}{\text{ }} \to {\text{2}}$We know that displacement by time taken is velocity. $ \Rightarrow v = \dfrac{d}{t}$Substituting the above in equation 2$ \Rightarrow P = F \times v$V is the velocity.Hence it is proved that power is the product of force and velocityGiven that,Mass of the body, $m = 10Kg$Acceleration of the body, $10{\text{ m/s}}$Velocity of the body, $5{\text{ m/s}}$The power of the body=?Power of the body is given by the formula$ \Rightarrow P = F \times v$We know that force is the product of mass and acceleration.$ \Rightarrow P = m \times a \times v$m is the massa is the accelerationSubstituting the given value$ \Rightarrow P = m \times a \times v$$ \Rightarrow P = 10 \times 10 \times 5$$ \Rightarrow P = 500W$

Note The term power also exists in electricity, electric power is the rate of doing work when voltage is applied. When voltage is applied the work done is the product of voltage current and time. Then,

$ \Rightarrow P = \dfrac{W}{t}$$ \Rightarrow P = \dfrac{{VIt}}{t}$$ \Rightarrow P = VI$P is the powerI is the currentt is the time

Power is a change in energy with respect to time. One way to add energy to a system is to apply force in the direction of displacement. This means power manifests as an (applied force changing over time) (in the direction of displacement) plus (an applied force) (in the direction of a displacement changing with respect to time). The second part of this second term is clearly a velocity. With a constant force (so the first term goes to 0), we’re left with power equals force times velocity.

Force is defined as the interaction between two bodies, or it can also be defined as the push or pull experienced by an object when an external force acts on it. Force is expressed in terms of Newton.

This is the concept that is explained in Newton’s first law of motion.

Newton’s First Law: Consider an object with no force acting on it. If it is at rest, It will remain at rest; if it is moving, it will continue its motion in a straight line at a constant speed. The force exists through contact or non-contact way.

Examples of contact forces are pushing a box and kicking a ball while examples of non-contact force are gravitational force and electrostatic force.

Force = (Mass) (Acceleration)

Power is defined as the amount of energy consumed when work is done in unit time. Power can also be defined as the rate at which work is done.

Power = Work done/Time taken

Watt is the unit of power.

Example: A lift motor has to move a fully laden lift 4m between floors in 1.5s. The lift has a mass of 1850 kg (ignore friction).

The relation between Power, Force, and Velocity

Suppose force F is acting on a body for time t. If during this time the body moves along the direction of the applied force to a distance s, then work done by that force is, W = F x s

Again, power, P = W/t= = Fs/t = Fv … … … (1) [as we know, s = v/t]

So, power = applied force x velocity of the body

If the displacement of the body, instead of being along with the force, is along a direction making an angle θ with the applied force, then

P = Fv cos θ

This equation represents a scalar product of two vector quantities.

According to vector notation, P = F.v. … … … (2)

This equation gives the relation between power, force, and velocity.

Power, in case of rotational motion:

In the case of rotational motion, we know,

Work = torque x angular displacement

Power, P = W/t = (Torque x angular displacement) / time

So, Power, P = Torque x angular velocity.