Distance Time Rate Worksheet Welcome to Math 111 Algebra

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Distance Time Rate Worksheet document sample

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```							            Welcome to Math 111
Instructor: Alexandra Nichifor

Class Website:
http://www.math.washington.edu/~nichifor/111F06.htm

Please pick up a copy of the syllabus and today’s
handout
Worksheet 1:
Speed as a Rate of Change
Time t      Distance D
(minutes)   travelled (miles)
after time t
0          0
10         120
20         170
30           180
40           180
Q?: How far did the rocket travel
from 50min to 60min?                50           205
60           280
280-205=75
70           430
A: 75 miles                              75           550
Delta Notation:

• Greek letter Delta:               is shorthand for
“the change in”
Example:

How far did the rocket travel from 50min to 60min?

 D  280  205  75 miles
(over a duration of t  60  50  10 min)
Q: What was the average speed of the rocket from
t=50 min to t=60 min?
Shorthand
(=change
D       in…)
average speed = Change in distance 
Change in time        t

D 280  205 75
AS                   7.5        miles per minute
t   60  50   10
On the graph:
Moral: Average Speed (AS) from time t1 to time t2
=slope of the secant line thru the graph of the distance at points t1 & t2

Rise

D  75

t  10
Run
A rate of change is a measure of how fast a
quantity is changing with respect to time

Examples?
VIP Example: average speed is a rate of change of distance.

D
average speed = Change in distance 
Change in time       t

In general:
 Blah
Average Rate of Change of Blah =
Change in Blah

t
Change in time
Types of Rates of Change:

Actual (Instantaneous)
Average Rate of Change
(will study in Math 112)

Example: Actual speed,

Overall                Incremental
(from t=0 to later time)    (from t=a to t=b)

Example:                    Example:
Average Trip Speed (ATS)      Average Speed (AS)
distance so far D         change in distance  D
ATS                      AS                    
time so far    t          change in time    t
• Note: An overall rate of change (such as ATS) is
a special case of an incremental rate of change.
that is, one in which the initial time t1=0.
• Question: How do we measure the ATS on a
graph of distance?
For example, on our handout, what was the ATS
over the first hour?
• Answer: Compute the slope of the line from the
beginning of the graph (t1=0) to t2=60 min.
ATS=
Slope of
Diagonal
Line

Rise=350

Tip: Can pick any two points on this line to compute the slope!

Run=75
Answer: ATS over the first hour = 350 / 75 = 4.67 mpm = 280 mph
Note: Using the original two points: 280 / 60 =4.67 mpm
…To be continued on Friday…

Homework for Friday:

1. Familiarize yourself with the class rules by carefully
reading the syllabus and the class website.

2. Print the Lecture Handouts (and bring to class!)

3. Get the text, a ruler, and a scientific calculator.

4. Read and do the problems in the Prologue.

5. Start working on Worksheet 1.

```
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