Difference between revisions of "Forest UCM Energy KEnWork"

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Consider the Kinetic Energy's temporal rate of change assuming that the mass of the particle is constant
 
Consider the Kinetic Energy's temporal rate of change assuming that the mass of the particle is constant
  
: <math>\frac{dT}{dt} = \frac{m}{2} \frac{d v^2}{dt}</math>
+
: <math>\frac{dT}{dt} = \frac{m}{2} \frac{d}{dt}v^2</math>
 +
::<math>= \frac{m}{2} \frac{d}{dt}\vec v \cdot \vec v</math>
  
 
[[Forest_UCM_Energy#KE_.26_Work]]
 
[[Forest_UCM_Energy#KE_.26_Work]]

Revision as of 12:46, 15 September 2014

Definition of KE

For a single particle of mass m moving with a velocity v, the kinetic energy is defined as

[math]T \equiv \frac{1}{2} mv^2[/math]

Work Energy Theorem

Derivation

Consider the Kinetic Energy's temporal rate of change assuming that the mass of the particle is constant

[math]\frac{dT}{dt} = \frac{m}{2} \frac{d}{dt}v^2[/math]
[math]= \frac{m}{2} \frac{d}{dt}\vec v \cdot \vec v[/math]

Forest_UCM_Energy#KE_.26_Work