Linear Motion
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Linear Motion of Objects on Distance-Time Graphs
Distance vs. Time Graphs • Distance vs. time graphs tell you how far something has traveled in a certain time. Object at Rest
y-axis has the dependent variable 3.50 3.00 2.50 2.00 1.50 1.00 distance (meters) 0.50 0.00 0.00
1.00
2.00
3.00
4.00
5.00
time (seconds)
x-axis has the independent variable
6.00
Object at Rest • The graph for an object at rest is flat. • After each time the object is at the same distance meaning it has not moved.
Object at Rest 3.50 3.00 2.50 2.00 1.50 1.00 distance (meters) 0.50 0.00 0.00
1.00
2.00
3.00 time (seconds)
4.00
5.00
6.00
Constant Speed • An object at a constant speed is a diagonal straight line. • The distance increases the same amount from point to point.
Constant Speed 16.00 14.00 12.00 10.00 8.00 6.00 4.00 distance (meters) 2.00 0.00 0.00
1.00
2.00
3.00
4.00
time (seconds)
5.00
6.00
Accelerating Object (Speeding Up) • The shape of the graph for an accelerating object is curved. • The object covers more and more distance between each point if it is speeding up.
Accelerating Object 200.00 150.00 100.00 50.00 distance (meters) 0.00 0.00
1.00
2.00
3.00
4.00
time (seconds)
5.00
6.00
7.00
Negative Acceleration (Slowing Down) • For an object with negative acceleration the graph is curved and is getting flatter. • The object goes less distance from point to point.
Negative acceleration 200.00 180.00 160.00 140.00 120.00 100.00 80.00 60.00 40.00 (meters) distance 20.00 0.00 0.00 1.00
2.00
3.00
4.00
time (seconds)
5.00
6.00
7.00
Comparision of Speed • When comparing speed, the line with the steeper slope has a greater speed. • A line with a greater slope covers more distance from point to point.
Comparison of Speed 16 14 12 10 8 6 4 distance (meters) 2 0 0
1
2
3 time (seconds)
4
5
6
Acceleration Comparison • When comparing acceleration, the line that is curved the most has the greatest acceleration. • A line that is curved more covers more distance from point to point.
A
c
c
e
l e
r a
t i o
n
C
o
m
p
a
r i s
o
n
3 5 0 . 0 0
3 0 0 . 0 0
2 5 0 . 0 0
2 0 0 . 0 0
S
e r ie s
1
1 5 0 . 0 0
S
e r ie s
2
1 0 0 . 0 0 distance (meters) 5 0 . 0 0
0 . 0 0
0 . 0 0
2 . 0 0
4 . 0 0
t i m
e
( s e
c o
6 . 0 0
n
d
s )
8 . 0 0
Displacement Graphs • Displacement graphs show displacement vs. time. • Displacement graphs tell you about traveling in different directions. • A positive slope is traveling away from the start. • A negative slope is traveling back to the start. • A flat line is an object that is not moving.
Direction Comparison • A displacement of 0 is equal to the where you started from. • Each point tells you how far you are from where you started. • At 4 hours the object represented by the square turned around and went back to the starting point.
D
6
0
.0
0
5
0
.0
0
4
0
.0
0
3
0
.0
0
2
0
.0
0
1
0
.0
0
i r e
c t i o
n
C
o
m
p
a r i s o
n
displacement (kilometers) 0
.0
0
0
. 0
0
1
.0
0
2
. 0
0
3
t im
e
. 0
( h
0
o u
4
r s
.0
0
5
. 0
0
)
Change of direction
6
.0
0
S
e
r i e
s
2
S
e
r i e
s
1
S t o r y
g r a p h
2 0 0
1 8 0
1 6 0 S e r ie s 1 1 4 0 S e r ie s 2 1 2 0 S e r ie s 3 1 0 0
S e r ie s 4 S e r ie s 5
8 0
S e r ie s 6 6 0 S e r ie s 7 displacement (no units) 4 0
2 0
0 0
2 0
4 0
6 0
t im
e
8 0
( m
in u t e s )
1 0 0
1 2 0
1 4 0
Story Graph Explanation • At first the object is traveling at a fairly constant velocity, away from the starting point. (Series 1) • Then it turns and goes at a constant velocity back towards the starting position. (Series 2) • It changes directions again and goes away from the starting point at about the original constant velocity. (Series 3) • From about 55 minutes to 75 minutes it moves at a slower constant velocity. (Series 4) • From about 75 minutes to about 85 minutes the object does not move. (Series 5) • From about 85 to 110 minutes it accelerates in a positive direction. (Series 6) • From about 95 minutes until about 110 minutes its velocity is about the same as the original velocity and fairly constant. (Series 7)
Distance vs. Time Graphs • Distance vs. time graphs tell you how far something has traveled in a certain time. Object at Rest
y-axis has the dependent variable 3.50 3.00 2.50 2.00 1.50 1.00 distance (meters) 0.50 0.00 0.00
1.00
2.00
3.00
4.00
5.00
time (seconds)
x-axis has the independent variable
6.00
Object at Rest • The graph for an object at rest is flat. • After each time the object is at the same distance meaning it has not moved.
Object at Rest 3.50 3.00 2.50 2.00 1.50 1.00 distance (meters) 0.50 0.00 0.00
1.00
2.00
3.00 time (seconds)
4.00
5.00
6.00
Constant Speed • An object at a constant speed is a diagonal straight line. • The distance increases the same amount from point to point.
Constant Speed 16.00 14.00 12.00 10.00 8.00 6.00 4.00 distance (meters) 2.00 0.00 0.00
1.00
2.00
3.00
4.00
time (seconds)
5.00
6.00
Accelerating Object (Speeding Up) • The shape of the graph for an accelerating object is curved. • The object covers more and more distance between each point if it is speeding up.
Accelerating Object 200.00 150.00 100.00 50.00 distance (meters) 0.00 0.00
1.00
2.00
3.00
4.00
time (seconds)
5.00
6.00
7.00
Negative Acceleration (Slowing Down) • For an object with negative acceleration the graph is curved and is getting flatter. • The object goes less distance from point to point.
Negative acceleration 200.00 180.00 160.00 140.00 120.00 100.00 80.00 60.00 40.00 (meters) distance 20.00 0.00 0.00 1.00
2.00
3.00
4.00
time (seconds)
5.00
6.00
7.00
Comparision of Speed • When comparing speed, the line with the steeper slope has a greater speed. • A line with a greater slope covers more distance from point to point.
Comparison of Speed 16 14 12 10 8 6 4 distance (meters) 2 0 0
1
2
3 time (seconds)
4
5
6
Acceleration Comparison • When comparing acceleration, the line that is curved the most has the greatest acceleration. • A line that is curved more covers more distance from point to point.
A
c
c
e
l e
r a
t i o
n
C
o
m
p
a
r i s
o
n
3 5 0 . 0 0
3 0 0 . 0 0
2 5 0 . 0 0
2 0 0 . 0 0
S
e r ie s
1
1 5 0 . 0 0
S
e r ie s
2
1 0 0 . 0 0 distance (meters) 5 0 . 0 0
0 . 0 0
0 . 0 0
2 . 0 0
4 . 0 0
t i m
e
( s e
c o
6 . 0 0
n
d
s )
8 . 0 0
Displacement Graphs • Displacement graphs show displacement vs. time. • Displacement graphs tell you about traveling in different directions. • A positive slope is traveling away from the start. • A negative slope is traveling back to the start. • A flat line is an object that is not moving.
Direction Comparison • A displacement of 0 is equal to the where you started from. • Each point tells you how far you are from where you started. • At 4 hours the object represented by the square turned around and went back to the starting point.
D
6
0
.0
0
5
0
.0
0
4
0
.0
0
3
0
.0
0
2
0
.0
0
1
0
.0
0
i r e
c t i o
n
C
o
m
p
a r i s o
n
displacement (kilometers) 0
.0
0
0
. 0
0
1
.0
0
2
. 0
0
3
t im
e
. 0
( h
0
o u
4
r s
.0
0
5
. 0
0
)
Change of direction
6
.0
0
S
e
r i e
s
2
S
e
r i e
s
1
S t o r y
g r a p h
2 0 0
1 8 0
1 6 0 S e r ie s 1 1 4 0 S e r ie s 2 1 2 0 S e r ie s 3 1 0 0
S e r ie s 4 S e r ie s 5
8 0
S e r ie s 6 6 0 S e r ie s 7 displacement (no units) 4 0
2 0
0 0
2 0
4 0
6 0
t im
e
8 0
( m
in u t e s )
1 0 0
1 2 0
1 4 0
Story Graph Explanation • At first the object is traveling at a fairly constant velocity, away from the starting point. (Series 1) • Then it turns and goes at a constant velocity back towards the starting position. (Series 2) • It changes directions again and goes away from the starting point at about the original constant velocity. (Series 3) • From about 55 minutes to 75 minutes it moves at a slower constant velocity. (Series 4) • From about 75 minutes to about 85 minutes the object does not move. (Series 5) • From about 85 to 110 minutes it accelerates in a positive direction. (Series 6) • From about 95 minutes until about 110 minutes its velocity is about the same as the original velocity and fairly constant. (Series 7)
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