Calculus/Kinematics

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Kinematics

IntroductionEdit

Kinematics or the study of motion is a very relevant topic in calculus.

If   is the position of some moving object, and   is time, this section uses the following conventions:

  •   is its position function
  •   is its velocity function
  •   is its acceleration function

DifferentiationEdit

Average Velocity and AccelerationEdit

Average velocity and acceleration problems use the algebraic definitions of velocity and acceleration.

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ExamplesEdit

Example 1:

A particle's position is defined by the equation   . Find the
average velocity over the interval   .
  • Find the average velocity over the interval   :
   
 
 
Answer:   .

Instantaneous Velocity and AccelerationEdit

Instantaneous velocity and acceleration problems use the derivative definitions of velocity and acceleration.

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ExamplesEdit

Example 2:

A particle moves along a path with a position that can be determined by the function   . 
Determine the acceleration when   .
  • Find   .
 
  • Find   .
 
  • Find  
   
 
 
Answer:  

IntegrationEdit

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