Velocity of Particle 1 given Kinetic Energy Calculator

✖Kinetic Energy is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity.ⓘ Kinetic Energy [KE]			+10% -10%
✖Mass 2 is the quantity of matter in a body 2 regardless of its volume or of any forces acting on it.ⓘ Mass 2 [m₂]			+10% -10%
✖Velocity of Particle with Mass m2 is the rate at which particle (of mass m2) moves.ⓘ Velocity of Particle with Mass m2 [v₂]			+10% -10%
✖Mass 1 is the quantity of matter in a body 1 regardless of its volume or of any forces acting on it.ⓘ Mass 1 [m₁]			+10% -10%

✖Velocity of particle with mass m1 is the rate at which particle (of mass m1) moves.ⓘ Velocity of Particle 1 given Kinetic Energy [v₁]

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Velocity of Particle 1 given Kinetic Energy Solution

STEP 0: Pre-Calculation Summary

Formula Used

Velocity of Particle with Mass m1 = sqrt(((2*Kinetic Energy)-(Mass 2*Velocity of Particle with Mass m2^2))/Mass 1)
v₁ = sqrt(((2*KE)-(m₂*v₂^2))/m₁)
This formula uses 1 Functions, 5 Variables

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Velocity of Particle with Mass m1 - (Measured in Meter per Second) - Velocity of particle with mass m1 is the rate at which particle (of mass m1) moves.
Kinetic Energy - (Measured in Joule) - Kinetic Energy is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity.
Mass 2 - (Measured in Kilogram) - Mass 2 is the quantity of matter in a body 2 regardless of its volume or of any forces acting on it.
Velocity of Particle with Mass m2 - (Measured in Meter per Second) - Velocity of Particle with Mass m2 is the rate at which particle (of mass m2) moves.
Mass 1 - (Measured in Kilogram) - Mass 1 is the quantity of matter in a body 1 regardless of its volume or of any forces acting on it.

STEP 1: Convert Input(s) to Base Unit

Kinetic Energy: 40 Joule --> 40 Joule No Conversion Required
Mass 2: 16 Kilogram --> 16 Kilogram No Conversion Required
Velocity of Particle with Mass m2: 1.8 Meter per Second --> 1.8 Meter per Second No Conversion Required
Mass 1: 14 Kilogram --> 14 Kilogram No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

v₁ = sqrt(((2*KE)-(m₂*v₂^2))/m₁) --> sqrt(((2*40)-(16*1.8^2))/14)

Evaluating ... ...

v₁ = 1.41824841668467

STEP 3: Convert Result to Output's Unit

1.41824841668467 Meter per Second --> No Conversion Required

FINAL ANSWER

1.41824841668467 ≈ 1.418248 Meter per Second <-- Velocity of Particle with Mass m1

(Calculation completed in 00.020 seconds)

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Created by Nishant Sihag

Indian Institute of Technology (IIT), Delhi

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National Institute of Information Technology (NIIT), Neemrana

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Kinetic Energy of System

LaTeX Go Kinetic Energy = ((Mass 1*(Velocity of Particle with Mass m1^2))+(Mass 2*(Velocity of Particle with Mass m2^2)))/2

Kinetic Energy given Inertia and Angular Velocity

LaTeX Go Kinetic Energy given Inertia and Angular Velocity = Moment of Inertia*(Angular Velocity Spectroscopy^2)/2

Kinetic Energy given Angular Momentum

LaTeX Go Kinetic Energy given Angular Momentum = (Angular Momentum/2)/(2*Moment of Inertia)

< Kinetic Energy of System Calculators

Kinetic Energy given Angular Velocity

LaTeX Go Kinetic Energy given Angular Momentum = ((Mass 1*(Radius of Mass 1^2))+(Mass 2*(Radius of Mass 2^2)))*(Angular Velocity Spectroscopy^2)/2

Kinetic Energy of System

LaTeX Go Kinetic Energy = ((Mass 1*(Velocity of Particle with Mass m1^2))+(Mass 2*(Velocity of Particle with Mass m2^2)))/2

Kinetic Energy given Inertia and Angular Velocity

LaTeX Go Kinetic Energy given Inertia and Angular Velocity = Moment of Inertia*(Angular Velocity Spectroscopy^2)/2

Kinetic Energy given Angular Momentum

LaTeX Go Kinetic Energy given Angular Momentum = (Angular Momentum/2)/(2*Moment of Inertia)

Velocity of Particle 1 given Kinetic Energy Formula

LaTeX Go

Velocity of Particle with Mass m1 = sqrt(((2*Kinetic Energy)-(Mass 2*Velocity of Particle with Mass m2^2))/Mass 1)
v₁ = sqrt(((2*KE)-(m₂*v₂^2))/m₁)

How do we get Velocity of particle 1 in terms of K.E?

Kinetic energy is the work needed to accelerate a body of a given mass from rest to its stated velocity. Which is numerically written as half*mass *square of velocity for a given object. As Kinetic energy, KE, is a sum of the kinetic energy for each mass. So for known total Kinetic Energy and velocity of one particle, we can get velocity of other particle.

How to Calculate Velocity of Particle 1 given Kinetic Energy?

Velocity of Particle 1 given Kinetic Energy calculator uses Velocity of Particle with Mass m1 = sqrt(((2*Kinetic Energy)-(Mass 2*Velocity of Particle with Mass m2^2))/Mass 1) to calculate the Velocity of Particle with Mass m1, The Velocity of Particle 1 given Kinetic Energy formula is a method of calculating the velocity of a particle when we know the velocity of other particles and the total kinetic energy of the system. As total kinetic energy is the sum of the individual kinetic energy of both particles, so we are left with only one variable, and by solving the equation we obtain the required velocity. Velocity of Particle with Mass m1 is denoted by v₁ symbol.

How to calculate Velocity of Particle 1 given Kinetic Energy using this online calculator? To use this online calculator for Velocity of Particle 1 given Kinetic Energy, enter Kinetic Energy (KE), Mass 2 (m₂), Velocity of Particle with Mass m2 (v₂) & Mass 1 (m₁) and hit the calculate button. Here is how the Velocity of Particle 1 given Kinetic Energy calculation can be explained with given input values -> 1.418248 = sqrt(((2*40)-(16*1.8^2))/14).

FAQ

What is Velocity of Particle 1 given Kinetic Energy?

The Velocity of Particle 1 given Kinetic Energy formula is a method of calculating the velocity of a particle when we know the velocity of other particles and the total kinetic energy of the system. As total kinetic energy is the sum of the individual kinetic energy of both particles, so we are left with only one variable, and by solving the equation we obtain the required velocity and is represented as v₁ = sqrt(((2*KE)-(m₂*v₂^2))/m₁) or Velocity of Particle with Mass m1 = sqrt(((2*Kinetic Energy)-(Mass 2*Velocity of Particle with Mass m2^2))/Mass 1). Kinetic Energy is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity, Mass 2 is the quantity of matter in a body 2 regardless of its volume or of any forces acting on it, Velocity of Particle with Mass m2 is the rate at which particle (of mass m2) moves & Mass 1 is the quantity of matter in a body 1 regardless of its volume or of any forces acting on it.

How to calculate Velocity of Particle 1 given Kinetic Energy?

The Velocity of Particle 1 given Kinetic Energy formula is a method of calculating the velocity of a particle when we know the velocity of other particles and the total kinetic energy of the system. As total kinetic energy is the sum of the individual kinetic energy of both particles, so we are left with only one variable, and by solving the equation we obtain the required velocity is calculated using Velocity of Particle with Mass m1 = sqrt(((2*Kinetic Energy)-(Mass 2*Velocity of Particle with Mass m2^2))/Mass 1). To calculate Velocity of Particle 1 given Kinetic Energy, you need Kinetic Energy (KE), Mass 2 (m₂), Velocity of Particle with Mass m2 (v₂) & Mass 1 (m₁). With our tool, you need to enter the respective value for Kinetic Energy, Mass 2, Velocity of Particle with Mass m2 & Mass 1 and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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