**
Step 1:
**Identify whether you are being asked to find the Displacement or the Distance Traveled.

**
Step 2 (
****
Displacement
****
):
** Setup and evaluate a Definite Integral problem using the given velocity equation, *
v(t)
*, and the given time interval, [*
a
**
,
**
b
*].

**
Step 2 (
****
Total Distance
****
):
** Set your velocity equation equal to zero, *
v(t)
**
=
**
0
*,and solve for the times (*
x-values
*) that your equation *
could
* changes signs (+/–).

You will need to determine the places where the velocity equation changes form positive *
y-values
*to negative *
y-values
*or negative *
y-values
*to positive*
y-values
*. These are the places where you are potentially changing directions, you stop moving forward, positive velocity, and start moving backward, negative velocity or vice versa. Those moments will always occur at the zeros of your velocity equation.

These will be the places that you need to break apart your larger *
x-interval
*[*
a
**
,
**
b
*] into smaller *
x-intervals
*. You don’t really care if the *
y-values
*are positive or negative on either side of those zeros you just found (despite what some people might tell you). No matter what is happening on either side of those *
x-values
*you know at those *
x-values
*you were stopped for a moment, *
v(t)
**
=
**
0
*, which means you need to break your *
x-values
*at those moments regardless. With Total Distance you need to be able to treat all area as positive movement.

This means you will setup a separate Definite Integral problem for each of those smaller *
x-intervals
*. In Step 3 (Total Distance) you will take the *
absolute value
* of any region that gives you a negative result, and then add the results for all the regions in Step 4 (Total Distance).

**
Step 3 (
****
Total Distance
****
):
** Setup and evaluate the Definite Integrals based upon the smaller *
x-intervals
*you found in Step 2 (Total Distance). Remembering that any interval that provides you a negative result, you will need to take the *
absolute value
* of that portion before adding it to the other results.

**
Step 4 (
****
Total Distance
****
):
** Treat all results from Step 3 (Total Distance) as positive values, and then add those results together to get your final result for Total Distance.

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