Graphing Speed; Slope - Cstephenmurray

Name: _____________________

position (m)

25

This is what we call a linear graph, because the data creates a straight line.

run = ∆ x

20 15

slope =

=

run

∆x

Time (sec) 0 0.5 1 1.5 2

∆ y = rise

10 5 0 0

0.5

Slope has actual meaning in science – ∆y

Data

Position vs. Time

The graph on the right is a distance versus time graph. That means that it shows how far an object has traveled after so many seconds.

rise

Ch.1:4

Graphing Speed; Slope

Period: _____________________

y2 - y 1

=

=

2

2.5

Slope for the above graph:

(20 - 10)m (2 - 1) sec

x2 - x 1

1 1.5 time (sec)

Distance (m) 0 5 10 15 20

=

10m

=

The slope of a position vs. time graph

10m/s

is SPEED

1 sec

Graphing Conventions: The independent variable is always on the x-axis. The dependent variable is always on the y-axis.

Position vs. Time

Point 1 (2,2)

Point 2 (10,2)

Time is always an independent variable (x-axis).

Independent variable—Time Dependent variable—position

Dependent Position (m) variable

2.5

Linear graph.

2

Position vs. time graph, so slope = speed (position/time)

1.5 1

(Pick any two points) Slope = rise/run = ∆y/∆x =

0.5 0 0

2

4

6

8

10

Independent variable

Time (sec)

(2 - 2)m

12

(10 - 2) sec

Steep slope— fast speed

(5,35) fast speed

(0,5) 0

1

slope =

2

3

4

5 6 7 8 Time (sec)

9

10 11 12

∆y (35 - 5)m 30m = 6m/s = = ∆x (5 - 0)sec 5sec

www.aisd.net/smurray

=

Gradual slope — slow speed

0m

= 0 m/s

8 sec

Position vs. Time

Position (m)

Position (m)

Position vs. Time 40 35 30 25 20 15 10 5 0

The slope (speed) of a flat line is zero—no speed. The object is at rest.

40 35 30 25 20 15 10 5 0

slow speed

(10,15)

4

9

(0,5)

0

1

slope =

2

3

5 6 7 8 Time (sec)

10 11 12

∆y (15 - 5)m 10m = 1m/s = = ∆x (10 - 0)sec 10sec Copyright © 2004, C. Stephen Murray

1. Linear

A. The variable on the vertical axis (y-axis).

2. Independent variable

B. A type of graph that looks like a straight line.

3. Dependent variable

C. The measure of the steepness of a line.

4. Slope

D. The variable on the horizontal axis (xaxis).

km

meters sec

meters

sec

miles hour

Ch.1:4

cm sec

km min

meter sec2

Which is the independent variable? ___________________________

Position vs. Time

Position (m)

Which of the following are units for speed?

120

Which is the dependent variable? _____________________________

100

Where was the object at 4 seconds? ___________________________

80

Find the slope of the graph (must show work)

60 40 20 0 0

2

4

6 8 Time (sec)

10

12

When did the object reach 150 meters? ____________________

Distance vs. Time Distance (meters)

What does the slope you just found stand for? ___________________

350 300 250 200 150 100 50 0

Where was the object at 9 seconds? _______________________ Find the slope of the graph (must show work) ______________

0

1

2

3

4 5 6 7 Time (secs)

8

9

10 11

Which is the independent variable? ___________________________

Position vs. Time

18 16 14 12 10 8 6 4 2 0

What does the slope you just found stand for? ______________

Which is the dependent variable? _____________________________

Position (m)

Where was the object at 4 seconds? ___________________________ Find the slope of the graph (must show work)

0

1

2

3 4 Time (sec)

5

6

What does the slope you just found stand for? ___________________ Position vs. Time

C

The segment that shows fast speed: The segment that shows slow speed:

B

Position

The slope of this graph means:

Which graph segments fit the following:

A

At rest: Fast speed:

B

C

A

D

Slow speed: Going backwards: Going forward:

Time www.aisd.net/smurray

Copyright © 2004, C. Stephen Murray