Calculating Speed Speed (S) : distance traveled (d)

divided by the amount of time it takes to travel (t).

S = d tOR

S= d t

Units for SpeedAlways a distance unit by a time unit.

Examples: Cars: mi/h Jets: km/h Snails: cm/s Falling objects: m/s

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….

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

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….

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)

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

Graphing Speed: Distance vs. Time Graphs

Phoenix

Denver

Graphing Speed: Distance vs. Time Graphs

Answer Question #4

Graphing Speed: Distance vs. Time Graphs

3 h

600 km

Graphing Speed: Distance vs. Time Graphs

3 hours

600 km

Different Slopes Answer Question #5

0

1

2

3

4

5

6

7

8

1 2 3 4 5 6 7

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

Question

Below is a distance vs. time graph of my position during a race. What was my AVERAGE speed for the entire race?

0

2

4

6

8

10

12

14

0 1 2 3 4 5 6

Time (hr)

Dis

tan

ce (

km

)

Average Speed = Total distance/Total time = 12 km/6 hr= 2 km/hr

Run = 6 hr

Rise = 12 km

Let’s try one….

Question

Below is a distance vs. time graph for 3 runners. Who is the fastest?

0

1

2

3

4

5

6

7

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?

AccelerationAccelerationAcceleration – Acceleration – the rate at the rate at which speed/velocity changeswhich speed/velocity changes

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

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

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….

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…

Graphing Acceleration:Use Speed vs. Time Graph

0

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4

6

8

10

12

14

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

Graphing Acceleration continued: Speed vs. Time Graph

0

2

4

6

8

10

12

14

0 1 2 3 4 5 6

Time (s)

Sp

ee

d (

m/s

)

1)In Speed vs. Time graphs:Acceleration = Rise/Run = 4 m/s ÷ 2 s = 2 m/s2

Run = 2 s

Rise = 4 m/s

Remember when Graphing Speed: use Distance vs. Time Graphs

0

5

10

15

20

25

30

35

0 1 2 3 4 5

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.

Question #7:

0

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10

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

0

5

10

15

20

25

30

35

0 1 2 3 4 5

Time (s)

Dis

tan

ce

(m

)

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.

Comparing the graphs side-by-side…

Speed

Sp

eed

Distance- Time Graph

Stopped

(m)

(s)

Shows acceleration… Shows speed…