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