Average SpeedAverage Speed

Mrs. MartinezMrs. Martinez

Sixth GradeSixth Grade

Welcoming Work Welcoming Work ReviewReviewWhat is Force? What is Force? What is a balanced force? Describe by using arrows What is a balanced force? Describe by using arrows to draw a diagram. to draw a diagram. What is an unbalanced force? Describe by using What is an unbalanced force? Describe by using arrows to draw a diagram. arrows to draw a diagram.

Getting your brain gears turning.Getting your brain gears turning.What is a distance-time graph? What is a distance-time graph? What is Motion? What is Motion? What is the connection between Speed, Distance, What is the connection between Speed, Distance, and Time?and Time?

ForcesForces A A forceforce is a push or pull is a push or pull

that one body exerts on that one body exerts on another. A force can another. A force can cause the motion of an cause the motion of an object to change. There object to change. There are two types of forces:are two types of forces:

Balanced forceBalanced force – one in – one in which the net force is which the net force is zero.zero.

Unbalanced forceUnbalanced force – one – one in which the net force in which the net force has a numerical value.has a numerical value.

ForcesForces

+ 1 force - 1 force

Balanced Force

Net force = 0

+ 1 force - 2 force

Unbalanced Force

Net force = -1

+ 1 force

+ 1 force

Unbalanced Force

Net force = +2

Turn and Talk Turn and Talk

What is motion? What is motion?

What Is Motion?What Is Motion?

MotionMotion is when an object changes is when an object changes place or position. To properly describe place or position. To properly describe motion, you need to use the following:motion, you need to use the following:

Start and end position?Start and end position? Movement relative to what?Movement relative to what? How far did it go?How far did it go? In what direction did it go?In what direction did it go?

Motion Re-CapMotion Re-Cap When an object changes its position, motion has When an object changes its position, motion has

occurred.occurred.– Distance- Distance- How far an object has movedHow far an object has moved..– Displacement- Displacement- How far an object has moved How far an object has moved in in

relation torelation to its starting point its starting point..– Consider directionConsider direction

Example: Two runners travel along the same Example: Two runners travel along the same straightstraight path in a path in a straightstraight line for 500 meters. At line for 500 meters. At the end of the run their the end of the run their distancesdistances are the same are the same but their but their displacementsdisplacements are different. How can are different. How can this be so?this be so?

SPEED

Describes how fast an object is moving.

Describes how fast an object is moving.

What Is Speed? What Is Speed? SpeedSpeed is the distance is the distance

an object travels in a an object travels in a certain amount of time certain amount of time (relationship of all 3)(relationship of all 3)

To calculate speed, you To calculate speed, you use the following use the following formula:formula:

Speed (s) =Speed (s) =Distance(d)Distance(d)

Time (t)Time (t)

Speed- Speed- Distance an object travels Distance an object travels per unit of timeper unit of time

Relationships between speed, Relationships between speed, distance, and time:distance, and time:

Speed = Distance/ TimeSpeed = Distance/ Time = d/ t = d/ t Constant Speed- speed does not Constant Speed- speed does not

change over timechange over time Average Speed- speed of motion Average Speed- speed of motion

when speed is changingwhen speed is changingAvg Speed = Total Avg Speed = Total

Distance/ Total TimeDistance/ Total Time

Instantaneous Speed- speed at Instantaneous Speed- speed at any given moment in time any given moment in time (speedometer)(speedometer)

The 3 formulas for Speed, Time & Distance:

Using your W/B write them down without using your notes.

Speed = Distance

TimeTime =

Distance

SpeedDistance =Speed x Time

Remember them from

this triangle:

D

S T

Solving for Speed Solving for Time Solving for Distance

DON’T REMEMBER HUH? DON’T REMEMBER HUH? WELL LET’S REFRESH WELL LET’S REFRESH THAT MEMORY!THAT MEMORY!

http://www.youtube.com/watch?v=9x7hP5LM1UE

Turn and Talk: What is the Relationship between

speed, distance and time?

SpeedSpeed is the distance an object is the distance an object travels in a certain amount of timetravels in a certain amount of time

Average Speed =Total distanceTotal time

WB Time!WB Time!

Let’s check out your knowledge! Without Let’s check out your knowledge! Without using your notes answer:using your notes answer:

What is the formula for finding speed? What is the formula for finding speed?

What is the formula for finding time, What is the formula for finding time, using distance and speed? using distance and speed?

What is the formula for finding distance What is the formula for finding distance using speed and time? using speed and time?

Try thisTry this

Mrs. Martinez walks home from her Mrs. Martinez walks home from her sister’s house everyday. It takes her 4 sister’s house everyday. It takes her 4 minutes and her house is 240 meters minutes and her house is 240 meters away.What is her average speed? away.What is her average speed?

240 meters/ 4 minutes =240 meters/ 4 minutes =

60 meters per minute. 60 meters per minute.

Example Question 1Example Question 1

Jane drives at an average speed of Jane drives at an average speed of 45 mph on a journey of 135 miles.45 mph on a journey of 135 miles.How long does the journey take?How long does the journey take?

To find a time, we need to To find a time, we need to divide divide distance by speeddistance by speed..

135 miles ÷ 45 mph = 3 hours 135 miles ÷ 45 mph = 3 hours

Example Question 2Example Question 2

Chris cycles at an average speed of 8 Chris cycles at an average speed of 8 mph.mph.If he cycles for 6½ hours, how far If he cycles for 6½ hours, how far does he travel?does he travel?

To find a distance, we need to To find a distance, we need to multiply speed by timemultiply speed by time..

8 mph × 6.5 hours = 52 miles 8 mph × 6.5 hours = 52 miles

Example Question 3Example Question 3

Nikki has to travel a total of 351 miles. Nikki has to travel a total of 351 miles. She travels the first 216 miles in 4 hours.She travels the first 216 miles in 4 hours.(a) What is her average speed for the first (a) What is her average speed for the first part of the journey?part of the journey?

To find average speed, we need to To find average speed, we need to divide divide distance by timedistance by time..

216 miles ÷ 4 hours = 54 mph 216 miles ÷ 4 hours = 54 mph

Her average speed is the same for the Her average speed is the same for the whole of her journey.whole of her journey.

(b) How long does the whole journey (b) How long does the whole journey take?take?

To find time, we need to To find time, we need to divide divide distance by speeddistance by speed..

351 miles ÷ 54 mph = 6.5 hours 351 miles ÷ 54 mph = 6.5 hours

15 mins = 0•25 hourSo: 3 hours 15 mins = 3•25 hours

30 mins = 0•5 hourSo: 7 hours 30 mins = 7•5 hours

45 mins = 0•75 hourSo: 2 hours 45 mins = 2•75 hours

Reminder: How to change minutes into a decimal

D

S T

First work it out on your paper then show me on your WB.

A windsurfer travelled 28 km in 1 hour 45 mins.

Calculate his speed.

Speed =

DistanceTime

28 km

1•75 h

=

= 16 km/h

1 hour 45 mins

Answer: His speed was 16 km / Answer: His speed was 16 km / hourhour

2 hour 30 mins

Answer: He travelled 125 kmAnswer: He travelled 125 km

A salesman travelled at an average speed of 50 km/h for 2 hours 30 mins. How far did he travel?

D

S TDistance = Speed x Time

= 50 x 2•5

= 125 km

Answer: It took 9 hours 15 minutesAnswer: It took 9 hours 15 minutes

A train travelled 555 miles at an average speed of 60 mph. How long did the journey take?

D

S TTime =

DistanceSpeed

55560=

= 9•25 hours

= 9 hours 15 mins

Speed ProblemSpeed Problem

Suppose you ran 2 Suppose you ran 2 km in 10 min. What km in 10 min. What is your speed?is your speed?

S = S = 2 km2 km = 0.2 = 0.2 km/minkm/min

10 min10 min

Ways To Calculate SpeedWays To Calculate Speed Constant speedConstant speed is when you is when you

are traveling at the same rate are traveling at the same rate of speed, such as 55 mph of speed, such as 55 mph constantly on a highway.constantly on a highway.

Average speedAverage speed is taking the is taking the total distance traveled, and total distance traveled, and dividing by the total time it dividing by the total time it takes. Used for calculations takes. Used for calculations that involve changing speed.that involve changing speed.

Instantaneous speedInstantaneous speed is the is the speed at any one given point speed at any one given point in time. in time.

Sooo… What is the Sooo… What is the formula for speed? formula for speed?

http://www.youtube.com/watch?feature=endscreen&v=K_kzgW_OYX0&NR=1

Practice Question 1Practice Question 1

Jim travels 45 miles at 15 mph.Jim travels 45 miles at 15 mph.How long does it take him?How long does it take him?

45 miles/15 mph= 45 miles/15 mph=

3 hrs. 3 hrs.

Practice Question 2Practice Question 2

Jemimah walks at 4 mph for 2½ Jemimah walks at 4 mph for 2½ hours.hours.How far does she walk?How far does she walk?

She walked 10 miles. She walked 10 miles. 4 mph x 2.5 hrs= 10 miles4 mph x 2.5 hrs= 10 miles

Practice Question 3Practice Question 3

Jenny drives at a constant speed. In Jenny drives at a constant speed. In the first three hours she travels 81 the first three hours she travels 81 miles.miles.How far will she have travelled after 5 How far will she have travelled after 5 hours?hours?

She will travel 135 milesShe will travel 135 miles 27 mph for 5 hrs= 135 miles27 mph for 5 hrs= 135 miles

GRAPHING AVERAGE GRAPHING AVERAGE SPEEDSPEED

Using a Distance-Time GraphUsing a Distance-Time Graph

Graphing MotionGraphing Motion

Graph Graph distance distance on the y-on the y-axis and axis and time on time on the x-the x-axisaxis

Slope = Slope = riserise = = distancedistance = speed = speed

run timerun time

Graphing SpeedGraphing Speed Speed is usually Speed is usually

graphed using a line graphed using a line graph, and it depicts graph, and it depicts the distance and time.the distance and time.

TimeTime is the independent is the independent variable, and thus is variable, and thus is ALWAYS on the x-axis.ALWAYS on the x-axis.

DistanceDistance is the is the dependent variable, dependent variable, and is ALWAYS on the y-and is ALWAYS on the y-axis.axis.

Bass Boat Speed

0

20

50

65 65 65

45

15

00

10

20

30

40

50

60

70

1 2 3 4 5 6 7 8 9 10

Time (seconds)

Dis

tanc

e (m

eter

s)

Average SpeedAverage Speed

What is the AVERAGE speed of the bass boat depicted in the graph?

Average Speed = 125 meters = 15.6 m/s

8 seconds

Bass Boat Speed

0

20

50

65 65 65

85

100

125

0

20

40

60

80

100

120

140

1 2 3 4 5 6 7 8 9 10

Time (seconds)

Dis

tan

ce

(m

ete

rs)

Instantaneous SpeedInstantaneous Speed

Bass Boat Speed

0

20

50

65 65 65

85

100

125

0

20

40

60

80

100

120

140

1 2 3 4 5 6 7 8 9 10

Time (seconds)

Dis

tan

ce

(m

ete

rs) What is the

instantaneous speed of the bass boat at t=7 seconds?

Instantaneous Speed = 85 meters = 12.1 m/s

7 seconds

Speed GraphsSpeed Graphs

Bass Boat Speed

0

20

50

65 65 65

45

15

00

10

20

30

40

50

60

70

1 2 3 4 5 6 7 8 9 10

Time (seconds)

Dis

tan

ce

(m

ete

rs)

•In what time period is the bass boat speeding up? •In what time period is the bass boat slowing down?•When is the speed NOT changing?

Distance - Time GraphDistance - Time Graph

If something is not If something is not moving, a moving, a horizontal line is horizontal line is drawn.drawn.

If something starts If something starts out slow and then out slow and then speeds up, its speeds up, its change in speed change in speed can look like this.can look like this.

Learning CheckpointLearning CheckpointThis graph shows several stages of motion:

•Stage 1: 100 m in 10 s

•Stage 2: 50 m in 10 s

•Stage 3: 150 m in 20 s

Calculate the speed as indicated by each of the colors.

Calculate the average speed.

What is the total distance?

What is the displacement?

SolutionSolutionStage 1: S= d/ t

100 m/ 10 s= 10 m/s

Stage 2: S= d/t

50 m/ 10 s= 5 m/s

Stage 3: S= d/t

150 m/ 20 s= 7.5 m/s

Avg Speed= Tot d/ Tot t

300 m/ 40 s= 7.5 m/s

Distance = 300 meters

Displacement = 0 meters

3) At a daily basis, you rotate between classes. 3) At a daily basis, you rotate between classes. Draw a distance vs time graph illustrating the Draw a distance vs time graph illustrating the

distance you travel during class rotations here at distance you travel during class rotations here at school school

Video RecapVideo Recap

http://www.youtube.com/watch?v=Spz8WfmREDM&NR=1&feature=fvwp

Average Speed RecapAverage Speed Recap

http://www.youtube.com/watch?v=WxCgVNqfub8

Velocity Velocity

The speed of an object in a certain direction. The speed of an object in a certain direction.

VelocityVelocity

VelocityVelocity is the speed of an object, but the direction is the speed of an object, but the direction is also included. It is calculated the same as speed, is also included. It is calculated the same as speed, but you must include a direction in your answer.but you must include a direction in your answer.

Example: the bass boat was moving 12 mph Example: the bass boat was moving 12 mph toward the north.toward the north.

VelocityVelocity

V = velocity (meters/second)

d = distance (meters)

t = time (seconds)

V = velocity (meters/second)

d = distance (meters)

t = time (seconds)

d d V =V = ttspeed of an object in a certain direction.

speed of an object in a certain direction.

VelocityVelocityspeed of an object in a certain direction.

speed of an object in a certain direction.

seconds

0

2

13

VelocityVelocity

The speed The speed and directionand direction of an of an object’s motion.object’s motion.– 88 km / hr southwest88 km / hr southwest

Speed=? Velocity=?Speed=? Velocity=?

16 meters

12 meters

20 meters

Total time=

4 seconds

Total time=

4 seconds

AccelerationAcceleration

AccelerationAcceleration is the is the rate of change of rate of change of velocity. A change velocity. A change in velocity can be in velocity can be either a change in either a change in speed, or speed, or direction, or both.direction, or both.

DecelerationDeceleration is is when acceleration when acceleration has a negative has a negative value.value.

AccelerationAcceleration The formula for calculating acceleration is:The formula for calculating acceleration is:

Acceleration (a) = Acceleration (a) = final velocity (vfinal velocity (vff) – initial velocity (v) – initial velocity (vii))

time (sec)time (sec)

The unit for velocity, in this case, is The unit for velocity, in this case, is

m/s/s OR m/sm/s/s OR m/s22

Acceleration Math ProblemAcceleration Math Problem

A jet starts at rest at the end of a A jet starts at rest at the end of a runway and reaches a speed of runway and reaches a speed of 80 m/s in 20 s. What is its 80 m/s in 20 s. What is its acceleration?acceleration?

a = a = 80 m/s - 0 m/s 80 m/s - 0 m/s = 4 = 4 m/sm/s22

20 s20 s

Acceleration Math ProblemAcceleration Math Problem

A skateboarder is moving in a A skateboarder is moving in a straight line at a speed of 3 m/s and straight line at a speed of 3 m/s and comes to a stop in 2 sec. What is his comes to a stop in 2 sec. What is his acceleration?acceleration?

a = a = 0 m/s - 3 m/s0 m/s - 3 m/s = -1.5 m/s = -1.5 m/s22

2 m/s2 m/s

InertiaInertia Inertia is the tendency Inertia is the tendency of an object to resist of an object to resist any change in motion. any change in motion. Put in another way, if Put in another way, if an object is moving, it an object is moving, it will keep moving until will keep moving until an outside force acts an outside force acts on it. on it.

Inertia is related to Inertia is related to mass: the greater the mass: the greater the mass of an object, the mass of an object, the greater its inertia.greater its inertia.

Newton’s 1Newton’s 1stst Law of Motion Law of Motion

Newton’s 1Newton’s 1stst Law Law is also known as is also known as the law of inertia. It says:the law of inertia. It says:

An object in motion will stay in An object in motion will stay in motion, and an object at rest will motion, and an object at rest will stay at rest, unless acted upon by stay at rest, unless acted upon by an outside force.an outside force.

Example: if you are approaching Example: if you are approaching a fence on a running horse, and a fence on a running horse, and the horse suddenly stops, you will the horse suddenly stops, you will keep going forward over the keep going forward over the horse’s head unless you are horse’s head unless you are wearing a seatbelt! (I don’t care wearing a seatbelt! (I don’t care who you are – that’s funny!)who you are – that’s funny!)

InertiaInertia

What does a seat belt do for us,What does a seat belt do for us, in terms of inertia?in terms of inertia?

-it helps us OVERCOME inertia!-it helps us OVERCOME inertia!

http://www.cimt.plymouth.ac.uk/projects/mepres/book8/bk8i18/bk8_18i2.htm

http://baldragon.ea.dundeecity.sch.uk/Departments/Physics/Movementint1/Averagespeedweb.htm