Rectilinear Motion

 

Time: t

Position: s

Speed: v

Acceleration: a

Lemma:

Method for integration:

 

1.      Check to see if there are only two variables

2.      If you have only two variables, see if you can separate the variables (SV)

3.      If you have more than two variables or if your variables are not the ones you are looking for, use the lemma to see if you can work around the problem

4.      Once you have separated the variables, then integrate (I)

 

Acceleration as a function of time: a=f(t)

C and D are constants of integration evaluated from initial conditions

 

Example 1

 

Acceleration as a function of velocity: a=f(v)

If you can solve to get v=k(t), then

or by using the lemma

 

Example 2

 

Acceleration as a function of position: a=f(s)

 

Example 3

 

Derivatives to know:

 

The chain rule for derivatives:

 

Example 4

 

Integrals to know:

 

Change of variables: Given a function U(x), one can use to change the variable of integration from x to U for an integral of the form

 

Example 5

 

Integration by parts:

 

 

Example 6

 


Mehrdad Negahban and the University of Nebraska, 1999-2000.

All rights reserved

Copy and distribute freely for personal use only

 

Department of Engineering Mechanics, University of Nebraska, Lincoln, NE 68588-0526