Title: Apr 24­10:38 AM (1 of 42)
November 18 2008
1.
Lab reports will be collected today
2.
Any late Speed/Distance/Time assignments handed in NOW
3.
Thursday, November 20
There will be a test on Speed problems on Thursday, November 20
Title: Apr 24­9:17 AM (2 of 42)
Graphing Motion
Discuss Questions #1­6, Page 365
1.
Explain why a graph is sometimes more useful than an equation.
Title: Apr 24­9:17 AM (3 of 42)
2.
What does the slope of a distance­time graph represent?
Slope refers to the steepness of a graph. The slope of a Distance/Time graph will be equal to the speed of the moving object.
Title: Nov 16­5:47 PM (4 of 42)
3.
What interpretation can be made about a moving car if the line on
a distance­time graph for the car has the following characteristics?
a) A high, or steep slope?
Title: Apr 24­9:21 AM (5 of 42)
b)
A low, or less steep slope?
Title: Apr 24­9:23 AM (6 of 42)
c)
A zero slope?
(what does a zero slope look like?)
Title: Apr 24­9:24 AM (7 of 42)
d)
A short line on the graph?
Title: Apr 24­9:28 AM (8 of 42)
e)
A long line on the graph?
Title: Apr 24­9:30 AM (9 of 42)
What would this graph tell you about the movement of an object?
Title: Apr 24­9:31 AM (10 of 42)
4.
Sketch a distance­time graph for a car cruising at 80 km/h
*First, create a table of values.
Time (hours)
0
1
2
3
4
5
6
7
8
Title: Apr 24­9:32 AM (11 of 42)
Distance (km)
0
80
160
240
320
400
480
560
640
Distance/Time Graph of a Car Travelling 80 km/h
640
560
480
400
320
240
160
80
Distance (km)
1
Title: Apr 28­9:19 AM (12 of 42)
2
3
4
5
6
Time (h)
7
8
How would the graph change if the car stopped for one hour after 320 km, and then continued on at 120 km per hour for three more hours?
(just do a rough sketch)
Time
Title: Apr 28­9:26 AM (13 of 42)
Distance/Time Graph of a Car Treavelling 80 km/h
720
640
560
480
400
320
240
160
80
Distance (km)
1
Title: Apr 28­9:19 AM (14 of 42)
2
3
4
5
6
Time (h)
7
8
5.
A car leaves Borden­Carlton, PEI, on its way across the Confederation Bridge into New Brunswick. The distances and times
from the toll booth in PEI are listed Table 4. They include a short
stretch of road beyond the end of the 12.9 km bridge.
A) Plot a distance­time graph using the information in Table 4.
Draw a line of best fit.
Title: Apr 28­9:33 AM (15 of 42)
Distance/Time Graph of a Car Treavelling
Across the Confederation Bridge
16
14
12
10
8
6
4
2
Distance (km)
2
Title: Apr 28­9:19 AM (16 of 42)
4
6
Time (min)
8
10
12
B)
Using your graph, find the distance travelled after 5.0 minutes.
Title: Apr 28­9:37 AM (17 of 42)
Distance/Time Graph of a Car Treavelling
Across the Confederation Bridge
16
14
12
10
8
6
4
2
Distance (km)
2
Title: Apr 28­9:19 AM (18 of 42)
4
6
Time (min)
8
10
12
C) Using your graph, find the time required to cross the bridge.
Title: Apr 28­9:37 AM (19 of 42)
Distance/Time Graph of a Car Treavelling
Across the Confederation Bridge
16
14
12
10
8
6
4
2
Distance (km)
2
Title: Apr 28­9:19 AM (20 of 42)
4
6
Time (min)
8
10
12
D) Was the speed constant during the car's trip across the bridge?
How do you know?
E) Calculate the slope of the graph? What does this slope represent?
Title: Apr 28­9:37 AM (21 of 42)
F)
What is the speed of the car in kilometers per hour?
Title: Apr 28­9:51 AM (22 of 42)
Distance/Time Graph of a Car Treavelling
Across the Confederation Bridge
16
14
12
10
8
6
4
2
Distance (km)
2
Title: Apr 28­9:19 AM (23 of 42)
4
6
Time (min)
8
10
12
6)
In Figure 5, the motion of two bicycle riders, Tom and Jerry,
is described on a distance­time graph.
Title: Apr 28­9:52 AM (24 of 42)
Motion of Two Bicycle Riders
200
A) From a qualitative observation of the lines on the graph, which rider has the greater speed?
Jerry
180
160
140
120
100
Tom
80
60
40
20
5
Title: Apr 28­9:54 AM (25 of 42)
10
Time (s)
15
20
Motion of Two Bicycle Riders
200
B) Calculate the speed of each rider by determining the slope of each line. Jerry
180
160
Does this quantitative result match youranswer to (A)?
140
120
100
Tom
80
60
40
20
5
Title: Apr 28­9:54 AM (26 of 42)
10
Time (s)
15
20
Motion of Two Bicycle Riders
Find the slope of the line for Jerry:
200
Jerry
180
160
140
120
100
Tom
80
60
40
20
5
Title: Apr 28­9:54 AM (27 of 42)
10
Time (s)
15
20
Motion of Two Bicycle Riders
Find the slope of the line for Tom:
200
180
Jerry
160
140
120
100
Tom
80
60
40
20
5
Title: Apr 28­9:54 AM (28 of 42)
10
Time (s)
15
20
C) If one of the bicycle riders suddenly stopped, how would the graph of that rider change?
Time
e
Title: Apr 28­10:05 AM (29 of 42)
Distance vs. Displacement
When talking about speed, it is often better to use displacement rather than distance for the movement of an object. Distance is defined as the total amount of movement an object undergoes.
Displacement is defined as the straight line separation of an object from a fixed point of reference. When an object moves, the amount of movement will be its change in displacement relative to the point of reference.
Title: Apr 28­10:08 AM (30 of 42)
Distance vs. Displacement
9.0 m
If we use the Start point as our reference, what is the runner's
displacement right now?
What is the distance travelled after he runs the course? D =
6.0 m
What is the displacement at the end of movment? D = What is his change in displacement* after he finishes running?
*The symbol is used to represent "change"
D =
9.0 m
Title: Apr 28­10:08 AM (31 of 42)
Finish
Distance vs. Displacement
What would a distance­time graph look like if you walked away from
the point of reference, then turned and walked straight back? Time
Time
Title: Apr 28­10:08 AM (32 of 42)
lacement
Distance
How would a displacement­time
graph look different?
Distance vs. Displacement
When would distance travelled be the same as D? (change in displacement?) Title: Apr 28­10:08 AM (33 of 42)
Distance vs. Displacement
What does a downward (negative) slope on a displacement ­ time graph mean?
Title: Apr 28­10:08 AM (34 of 42)
Think you understand how speed, distance, and time are expressed graphically?
It's time for the Motion Match Challenge!
Title: Apr 28­10:08 AM (35 of 42)
GLX Challenge
1)
Get into groups of three
2)
Using the GLX units, try to duplicate each of the following displacement ­ time graphs
3)
You must show me each graph once you have duplicated it before you get the next one
4)
The easiest way to do this is for one person to hold and control the GLX, one person hold the
motion sensor, and the third person to move
Title: Apr 28­10:08 AM (36 of 42)
GLX Challenge
1)
Time
nt
Title: Apr 28­10:08 AM (37 of 42)
GLX Challenge
2)
Time
nt
Title: Apr 28­10:08 AM (38 of 42)
GLX Challenge
3)
Time
nt
Title: Apr 28­10:08 AM (39 of 42)
GLX Challenge
4)
Time
nt
Title: Apr 28­10:08 AM (40 of 42)
Homework
Complete the Graphing Introduction sheet handed out during class.
Title: Apr 28­10:08 AM (41 of 42)
Title: Nov 16­6:28 PM (42 of 42)