Speed vs. Velocity

Speed vs. VelocitySpeed vs. Velocity

Reviewing Key Concepts pg. Reviewing Key Concepts pg. 3473471a. 1a. What is speed?What is speed?

Speed is distance traveled per unit Speed is distance traveled per unit time.time.

b. b. What is the average speed of a car What is the average speed of a car that travels 160 km in 2 hours?that travels 160 km in 2 hours?

80 km/h80 km/h

c. c. If you walked at an average speed If you walked at an average speed of 1.2 m/s, how long would it take of 1.2 m/s, how long would it take to cross a road that is 16-m wide?to cross a road that is 16-m wide?16 m1.2 m/s

= 13 1/3 s

Note: units

m m sm 1 ms

= ∙

2a. 2a. What is velocity?What is velocity?Velocity is speed in a given Velocity is speed in a given direction.direction.

b.b. Describe the two ways in which Describe the two ways in which velocity can change.velocity can change.Velocity can change in speed or Velocity can change in speed or direction or both.direction or both.

c. c. Your car’s speedometer reads a Your car’s speedometer reads a constant 35 mi/hr. Can you say your constant 35 mi/hr. Can you say your velocity isvelocity is constant? Explain.constant? Explain.Probably not. The question does not Probably not. The question does not give information about change (or give information about change (or no change) in direction. Velocity no change) in direction. Velocity involves both speed and direction. involves both speed and direction.

3a. 3a. What does the slope of a distance-What does the slope of a distance-versus-time graph show you about versus-time graph show you about the motion of an object?the motion of an object?The slope of a distance-versus-time The slope of a distance-versus-time graph shows you the speed of the graph shows you the speed of the moving object.moving object.

b. b. The rise of a line on a distance-The rise of a line on a distance-versus-time graph is 600 m and run versus-time graph is 600 m and run is 3 minutes. What is the slope of is 3 minutes. What is the slope of the line?the line?The slope is 200 m/min.The slope is 200 m/min.

Activity Activity 7575

TitleTitle: Interpreting Motion : Interpreting Motion GraphsGraphs

When you measured the speed of a When you measured the speed of a cart rolling down a track, do you think cart rolling down a track, do you think the carts were going the same speed the carts were going the same speed the whole time?the whole time? The cart started at rest (0 cm/s)The cart started at rest (0 cm/s) It then sped up to its top speed down the It then sped up to its top speed down the

rampramp It eventually slowed down until it stopped It eventually slowed down until it stopped

came to rest (0 cm/s)came to rest (0 cm/s) You found the AVERAGE SPEEDYou found the AVERAGE SPEED INSTANTANEOUSINSTANTANEOUS SPEED is the speed at SPEED is the speed at

any given moment in time any given moment in time (speedometer).(speedometer).

In this activity...In this activity...

You will analyze graphs of distance You will analyze graphs of distance versus time that show motion over a versus time that show motion over a whole trip.whole trip.

The motion may be different throughout The motion may be different throughout the trip.the trip.

Notice on pg. E-12, the road to school is Notice on pg. E-12, the road to school is a straight road and does not require any a straight road and does not require any turning. This activity focuses on linear turning. This activity focuses on linear motion only.motion only.

Read E-12Read E-12

Problem:Problem: How can you use a graph to How can you use a graph to describe motion?describe motion?

Hypothesis:Hypothesis: If you _____________, then If you _____________, then you ____________________.you ____________________.

What do you know about What do you know about reading a motion graph?reading a motion graph?

Time (hr)

Dis

tanc

e (m

i)

x-axis is time

Y-axis is distance

ProcedureProcedure

Trip Slips – figure out where they go on the graphs!

You will be exploring how the slope on the graph relates to speed. You will also analyze graphs of distance versus time that show motion over a whole trip, as opposed to determining one average speed over a trip

What do the changes in the graph’s slopes on a distance-versus-time graph mean?

Background informationBackground information:: A straight line indicates a constant A straight line indicates a constant

speed.speed. A positive (upward) slope means the A positive (upward) slope means the

car is moving away from the reference car is moving away from the reference point (home), or positive velocitypoint (home), or positive velocity

A zero slope (horizontal line) is a A zero slope (horizontal line) is a stopped car.stopped car.

A negative (downward) slope is a car A negative (downward) slope is a car moving back toward the reference moving back toward the reference point (home), or negative velocity.point (home), or negative velocity.

Background cont.:Background cont.: A steeper slope indicates a faster A steeper slope indicates a faster

speed.speed. A curved line of changing slope A curved line of changing slope

indicates linear acceleration, or change indicates linear acceleration, or change in speed.in speed.

The rate of curvature defines the The rate of curvature defines the amount of acceleration.amount of acceleration.

SlopeSlope

Slope = the change in y (∆y)

the change in x (∆x)

the change in the distance (∆d)

the time interval (∆t) =

Procedure step #5Procedure step #5 Put your explanation of each persons trip on Put your explanation of each persons trip on

the back of your template or on separate the back of your template or on separate paperpaper

Data/observation:Data/observation:

Explanations:Teasha’s Trip:D- The slope of the line is 3 mi/6 min or 0.5 mi/min,

which shows the car took 6 minutes to travel 3 miles.

Josh’s Trip:

DiscussionDiscussion

Are Teasha’s and Josh’s graphs realistic?

Do cars usually change speed instantaneously?

What would be a more realistic way to draw the graphs?

Time

Dis

tanc

e

Time

Dis

tanc

eNot Realistic Realistic

Analysis Question #5Analysis Question #5

An object accelerates if it has a An object accelerates if it has a change in speed or direction.change in speed or direction.

A distance vs. time graph with a A distance vs. time graph with a constant slope shows that the speed constant slope shows that the speed is constant.is constant.

If the slope is increasing, the speed is If the slope is increasing, the speed is increasing and the car is increasing and the car is accelerating.accelerating.

Time

Dis

tanc

e

Time

Dis

tanc

eAcceleration:

slope is increasing

Deceleration:

slope is decreasing

Graphing Speed: Graphing Speed: Distance vs. Time GraphsDistance vs. Time Graphs

0

200

400

600

800

1000

1200

1400

1600

2 3 4 5 6 7

Dis

tanc

e (K

m)

Time (hr)

200

Phoenix

Denver

Average speedAverage speed

• Speed is usually NOT CONSTANT– Ex. Cars stop and go regularly– Runners go slower uphill than downhill

• Average speed = total distance traveled/total time it took.

Calculating Average Speed Calculating Average Speed • 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

• Ave. Speed:total d/total t = 60 km/3 h = 20 km/h

QuestionQuestion• 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

VelocityVelocity

• Velocity – the SPEED and DIRECTION of an object.

– Example: • An airplane moving North at 500 mph• A missile moving towards you at 200 m/s



3 h

600 km


3 hr

600 km

Different SlopesDifferent Slopes

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



QuestionQuestion

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

QuestionQuestion

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

Leroy is the fastest. He completed the race in 3 hours

AccelerationAcceleration

Acceleration = Acceleration = speeding up? speeding up? Acceleration – Acceleration – the rate at the rate at

which velocity changeswhich velocity changes Can be an:Can be an:

Increase in speedIncrease in speed Decrease in speedDecrease in speed Change in directionChange in direction

Types of accelerationTypes of acceleration 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

Changing DirectionChanging Direction Example: Car takes turn (can be at Example: Car takes turn (can be at

constant speed)constant speed)

screeeeech

QuestionQuestion

How can a car be accelerating if How can a car be accelerating if its speed is a constant 65 km/h?its speed is a constant 65 km/h?

If it is changing directions it is If it is changing directions it is acceleratingaccelerating

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

48

8

16

24

32

40

Time (s)

4 m/s

Calculating Speed Worksheet

Documents

Speed vs. Velocity