411 REFERENCE · Wikibooks
Calculus/Kinematics
Reference material by Wikibooks contributors. This retains its source identity and is not 411 news reporting.
Centre of mass Parametric and Polar Equations
Introduction
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
Differentiation
Average Velocity and Acceleration
Average velocity and acceleration problems use the algebraic definitions of velocity and acceleration.
Examples
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 Acceleration
Instantaneous velocity and acceleration problems use the derivative definitions of velocity and acceleration.
Examples
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:
Integration