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Calculating Speed Speed (S) : distance traveled (d)
divided by the amount of time it takes to travel (t).
S = d tOR
S= d t
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Units for SpeedAlways a distance unit by a time unit.
Examples: Cars: mi/h Jets: km/h Snails: cm/s Falling objects: m/s
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If I travel 100 kilometer in one hour then I have a speed of…
100 km/h
If I travel 1 meter in 1 second then I have a speed of….
1 m/s
S = d/tLet’s
practice….
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Average speed Average speed = total distance
traveled total time.
Do your parents always drive at the same speed? NO!!
So, Speed is usually NOT CONSTANT, so we use “average
speed” Examples: Cars stop at stoplights and speed up on the highway Runners go slower uphill than downhill
Now, write your answer for Question #1
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It took me 1 hour to go 40 km on the highway. Then it took me 2 more hours to go 20 km using the streets.
Total Distance: 40 km + 20 km = 60 km
Total Time: 1 h + 2 h = 3 hr
Avg. Speed: total d/total t = 60 km/3 h = 20 km/h
timeTotal
DistTotalSpeedAvg
_
.__.
Let’s practice….
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Question
I ran 1000 m in 3 minutes. Then ran another 1000 m uphill in 7 minutes. What is my average speed? A) 100 m/min B) 2000 m/min C) 10 m/min D) 200 m/min E) 20 m/min
Total Dist. = 1000 m + 1000 m = 2000 m
Total Time = 3 min + 7 min = 10 min
Ave speed = total dist/total time =
2000m/10 min = 200 m/min = D
Here’s one for you to try…. (Question
#2)
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VelocityVelocity – the SPEED and
DIRECTION of an object.
Examples: An airplane moving North at 500 mph A missile moving towards you at 200 m/s
Answer Question #3
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Graphing Speed: Distance vs. Time Graphs
Phoenix
Denver
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Graphing Speed: Distance vs. Time Graphs
Answer Question #4
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Graphing Speed: Distance vs. Time Graphs
3 h
600 km
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Graphing Speed: Distance vs. Time Graphs
3 hours
600 km
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Different Slopes Answer Question #5
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Time (hr)
Dis
tan
ce (
km
)
Run = 1 hr
Run = 1 hr
Run = 1 hr
Rise = 0 km
Rise = 2 km
Rise = 1 km
Slope = Rise/Run= 1 km/1 hr= 1 km/hr
Slope = Rise/Run= 0 km/1 hr= 0 km/hr
Slope = Rise/Run= 2 km/1 hr= 2 km/hr
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Question
Below is a distance vs. time graph of my position during a race. What was my AVERAGE speed for the entire race?
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0 1 2 3 4 5 6
Time (hr)
Dis
tan
ce (
km
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Average Speed = Total distance/Total time = 12 km/6 hr= 2 km/hr
Run = 6 hr
Rise = 12 km
Let’s try one….
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Question
Below is a distance vs. time graph for 3 runners. Who is the fastest?
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0 1 2 3 4 5 6 35
Time (h)
Dis
tan
ce (
mi.
)
Bob
Jane
Leroy
Leroy is the fastest. He completed the race in 3 hours
What do you think?
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AccelerationAccelerationAcceleration – Acceleration – the rate at the rate at which speed/velocity changeswhich speed/velocity changes
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Acceleration can be a(n):Acceleration can be a(n):Increasing speedIncreasing speed– Example: Car speeds up at green lightExample: Car speeds up at green light
Decreasing speedDecreasing speed– Example: Car slows down at stop lightExample: Car slows down at stop light
Change in DirectionChange in Direction– Example: Car takes turn (can be at Example: Car takes turn (can be at
constant speed)constant speed)
screeeeech
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Calculating AccelerationCalculating AccelerationIf an object is moving in a straight lineIf an object is moving in a straight line
Time
SpeedInitialspeedFinala
__
Units of acceleration:Units of acceleration:
m/sm/s2, 2, mphmph22
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0 s 1 s 2 s 3 s 4 s
0 m/s 4 m/s 8 m/s 12 m/s 16 m/s
2/4
4
/0/16
__
sm
s
smsmTime
SpeedInitialSpeedFinalonAccelerati
Let’s try one together….
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Question #6Question #6
A skydiver accelerates from 20 m/s to 40 A skydiver accelerates from 20 m/s to 40 m/s in 2 seconds. What is the skydiver’s m/s in 2 seconds. What is the skydiver’s average acceleration?average acceleration?
2/10
2
/20
2
/20/40
__
sm
s
sm
s
smsmTime
speedInitialspeedFinalAccel
Now, you try this one…
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Graphing Acceleration:Use Speed vs. Time Graph
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0 1 2 3 4 5 6
Time (s)
Sp
ee
d (
m/s
)
1)Inclined line= Speed is increasing with time or an increase in acceleration.
2)Line is straight = acceleration is constant3)Flat Line???? Constant Speed
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Graphing Acceleration continued: Speed vs. Time Graph
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Time (s)
Sp
ee
d (
m/s
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1)In Speed vs. Time graphs:Acceleration = Rise/Run = 4 m/s ÷ 2 s = 2 m/s2
Run = 2 s
Rise = 4 m/s
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Remember when Graphing Speed: use Distance vs. Time Graphs
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35
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Time (s)
Dis
tan
ce
(m
)
On Distance vs. Time graphs1) Curved line= shows the object is accelerating.**Remember slope = speed, so a curved line also means
your speed is increasing because your slope is increasing.
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Question #7:
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12
14
0 1 2 3 4 5 6
Time (s)
Sp
ee
d (
m/s
)
Above is a graph showing the speed of a car over time.1) How is the speed of the car changing (speeding up,
Slowing down, or staying the same)?2) What is this car’s acceleration?
1) The car is slowing down2) Acceleration = 0 – 12 / 6 = -12m/s ÷6s = -2 m/s2
Run = 3 s
Rise = -6 m/s
Graphing Acceleration continued: Speed vs. Time Graph
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35
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Time (s)
Dis
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(m
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1)Which line represents an object that is accelerating?
The black and red lines represent objects that are accelerating. Black is going a greater distance each second, so it must be speeding up. Red is going less each second, so what do you think it is doing?
Remember: in distance vs. time graphs: curved line = accelerating, straight line = constant
speed
Pop Quiz!!
Time (s)
Slowing down
Hint: Check out the x and y axes labels.
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Comparing the graphs side-by-side…
Speed
Sp
eed
Distance- Time Graph
Stopped
(m)
(s)
Shows acceleration… Shows speed…