**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

** **

** **

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

_{}

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

_{}

or by using the lemma

_{}

** **

** **

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

_{}

_{}

** **

** **

**Derivatives to know:**

_{}

_{}

** **

**The chain rule for derivatives:**

_{}

** **

** **

**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

_{}

** **

** **

**Integration by parts: **

_{}

** **

ã 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