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Kinetic Energy and WorkEnergy Theorem
The workenergy theorem states that the work done by all forces acting on a particle equals the change in the particle's kinetic energy.
Learning Objective

Discuss the relationship between Newton's Second Law and workenergy theorem
Key Points

The work W done by the resultant force on a particle equals the change in the particle's kinetic energy E_{k}:
$W=\Delta E_k=\frac{1}{2}mv_f^2\frac{1}{2}mv_i^2$ . 
The workenergy theorem can be derived from Newton's second law.

Work transfers energy from one place to another or one form to another. In more general systems than the particle system mentioned here, work can change the potential energy of a mechanical device, the heat energy in a thermal system, or the electrical energy in an electrical device.
Term

torque
A rotational or twisting effect of a force; (SI unit newtonmeter or Nm; imperial unit footpound or ftlb)
Full Text
Work in general transfers energy from one place to another or one form to another, and the following is an explanation of the workenergy principle as it applies to particle dynamics. It should be noted that in more general systems, work can change the potential energy of a mechanical device, the heat energy in a thermal system, or the electrical energy in an electrical device.
The WorkEnergy Theorem
The principle of work and kinetic energy (also known as the workenergy theorem) states that the work done by the sum of all forces acting on a particle equals the change in the kinetic energy of the particle . This definition can be extended to rigid bodies by defining the work of the torque and rotational kinetic energy.
The work W done by the resultant (net) force on a particle equals the change in the particle's kinetic energy E_{k}:
where v_{i} and v_{f} are the speeds of the particle before and after the change and m is the particle's mass.
Derivation
For the sake of simplicity, we will consider the case in which the resultant force F is constant in both magnitude and direction and is parallel to the velocity of the particle. The particle is moving with constant acceleration a along a straight line. The relationship between the net force and the acceleration is given by the equation F = ma (Newton's second law), and the particle's displacement d can be expressed by the equation:
which follows from the following kinematic equation:
The work of the net force is calculated as the product of its magnitude and the particle's displacement. Substituting the above equations yields:
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Key Term Reference
 Law
 Appears in this related concepts: Physics and Other Fields, Damped Harmonic Motion, and Models, Theories, and Laws
 acceleration
 Appears in this related concepts: Centripetial Acceleration, Position, Displacement, Velocity, and Acceleration as Vectors, and Applications and ProblemSolving
 displacement
 Appears in this related concepts: Calculus with Parametric Curves, Reference Frames and Displacement, and Interference
 energy
 Appears in this related concepts: Energy Transportation, Surface Tension, and Introduction to Work and Energy
 equation
 Appears in this related concepts: A General Approach, Equations and Inequalities, and Equations and Their Solutions
 force
 Appears in this related concepts: Work Done by a Variable Force, Driven Oscillations and Resonance, and Glancing Collisions
 heat
 Appears in this related concepts: Heat and Work, Work, and The First Law
 kinematic
 Appears in this related concepts: Motion with Constant Acceleration, Temperature, and Constant Acceleration
 kinematics
 Appears in this related concepts: Applications, Constant Angular Acceleration, and Defining Kinematics
 kinetic
 Appears in this related concepts: Friction: Static, The Kinetic Molecular Theory of Matter, and Sculpture
 kinetic energy
 Appears in this related concepts: Elastic Potential Energy, Elastic Collisions in One Dimension, and Inelastic Collisions in Multiple Dimensions
 magnitude
 Appears in this related concepts: Roundoff Error, Multiplying Vectors by a Scalar, and Components of a Vector
 mass
 Appears in this related concepts: Mass Spectrometer, Mass, and Pop Art
 net force
 Appears in this related concepts: Diffusion, ProblemSolving With Friction and Inclines, and The Second Law: Force and Acceleration
 parallel
 Appears in this related concepts: Charging a Battery: EMFs in Series and Parallel, Resistors in Parallel, and Combination Circuits
 potential
 Appears in this related concepts: What is Potential Energy?, Conservative and Nonconservative Forces, and Linear Expansion
 potential energy
 Appears in this related concepts: Escape Speed, Defining Graviational Potential Energy, and Types of Energy
 resultant
 Appears in this related concepts: Adding and Subtracting Vectors Graphically, TwoComponent Forces, and Forces in Two Dimensions
 rigid
 Appears in this related concepts: Connected Objects, The Physical Pendulum, and Center of Mass and Translational Motion
 rigid body
 Appears in this related concepts: Stability, Balance, and Center of Mass, Center of Mass and Inertia, and Motion of the Center of Mass
 velocity
 Appears in this related concepts: RootMeanSquare Speed, Arc Length and Speed, and Tangent and Velocity Problems
 work
 Appears in this related concepts: Force at an Angle to Displacement, Conservation of Energy in Rotational Motion, and Free Energy and Work
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Cite This Source
Source: Boundless. “Kinetic Energy and WorkEnergy Theorem.” Boundless Physics. Boundless, 29 Dec. 2014. Retrieved 27 Apr. 2015 from https://www.boundless.com/physics/textbooks/boundlessphysicstextbook/workandenergy6/workenergytheorem63/kineticenergyandworkenergytheorem2786249/