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DYNAMICS - THEORY

   

Many times, the motion of an object is specified by an acceleration that is constant with time. For example, an object that falls for a short distance in the earth's (or any other planet's) atmosphere experiences a constant acceleration. That constant is written as, ao,

     a = dv/dt = ao = constant

By integrating, the velocity can be determined as a function of the acceleration and time, giving

     

 
v(t) = vo + ao (t - to)
 

Next, the velocity can be integrated to express the position as a function of the acceleration and time, giving,

     

 
x(t) = xo + vo (t - to) + ao (t - to)2 / 2
 

Using the chain rule, the acceleration can be expressed as

     

This relationship can be integrated to express the velocity as a function of the acceleration and position.

     

 
v2 = vo2 + 2 ao (x - xo)
 

It should be stressed that above equations are only valid when the acceleration is expressed as a constant.

     
   
 
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