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Kinetic Energy

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Equation

(Eq1)     EK = 1 2 mu2

kinetic energy

Nomenclature

EK (or KE)	kinetic energy
m	mass
u (or v)	velocity
F	force
W	work

Quick
The kinetic energy of a particle is a scalar quantity; it depends only on the particle's mass and speed, not its direction of motion. A car (viewed as a particle) has the same kinetic energy when going north at 10 m/s as when going east at 10 m/s. Kinetic energy can never be negative, and it is zero only when the particle is at rest.


Details

Consider a mass that is initially at rest relative to the earth, which is taken as the coordinate frame. Let this system by acted on by an external horizontal force F that moves the mass a distance dx in the direction of the force. Thus, there is no change in potential energy. Let there be no heat transfer and no change in internal energy. Then from the first law, Eq5:

δW = −F dx = −d E_K

but:

F = ma = m

du dt

= m

dx dt

du dx

= mu

du dx

then:

dE_K = F dx = mu du

Integrating:

∫

EK   EK = 0

dEK =

∫

u   u = 0

mu du

(Eq1)

EK = 1 2 mu2