Negative 10 Miles per Hour?
1-1-2 Velocity and Speed
Velocity vs. Speed
• VELOCITY – change in DISPLACEMENT occurring over time– Includes both MAGNITUDE and DIRECTION
• VECTOR
• SPEED – change in DISTANCE occurring over time– Inclues ONLY MAGNITUDE
• SCALAR
Average Velocity/Speed Equations
t
dv
221 vv
vavg
average speed
or velocity
distanceor
displacement
time
average speed
or velocity
two velocitiesor speeds
...
...
21
21
tt
ddvavg
average speed
total distance
total time
Example #1Jim gets on his bike and rides 300 meters west
in 60 seconds.
What is his average velocity?
What is his average speed?
v = d / tv = 300 m / 60 sv= 5 m/s WEST
v = d / tv = 300 m / 60 s
v= 5 m/s
v = d / tv = -300 m / 60 s
v = -5 m/s
Example #2Sally gets up one morning and decides to take
a three mile walk. She completes the first mile in 8.0 minutes, the second mile in 8.5 minutes, and the third mile in 9.0 minutes.
What is her average speed?
total
totalavg t
dv
min12.0
min0.9min5.8min0.8
3 mimivavg
Example #3A car’s speed changes from 20 meters per
second to 10 meters per second.
What is its average speed?
221 vv
vavg
s
msm
sm
vavg 152
1020
How Graphs Show Velocity and SpeedPosition vs. Time
Time
Po
sit
ion
What is happening in thisgraph?
MotionlessObjectCONSTANT
ZEROSLOPE
How Graphs Show Velocity and Speed
What is happening in thisgraph?
Position vs. Time
Time
Po
sit
ion
CONSTANTPOSITIVE
SLOPE
Moving withCONSTANT
positive velocity
How Graphs Show Velocity and Speed
What is happening in thisgraph?
Position vs. Time
Time
Po
sit
ion
INCREASINGSLOPE
Moving withINCREASING
velocity
Find displacement
Using v-t GraphsVelocity vs. Time
-20
-15
-10
-5
0
5
10
15
20
25
30
35
0 1 2 3 4 5 6 7 8 9 10 11
Time (s)
Velo
cit
y (
m/s
)
Find distancetraveled
What can we DO with a v-t graph?
Find averagevelocity
How do you use the v-t graph to findAVERAGE VELOCITY?
How do you use the v-t graph to find DISTANCE TRAVELED?
How do you use the v-t graph to find DISPLACEMENT?
Area under the graph
Area on TOP and BOTTOMboth considered POSITIVE
Area under the graph
Area on TOP = POSITIVEArea on BOTTOM = NEGATIVE