1 speed and velocity what is speed, velocity and acceleration? speed and velocity (use with speed,...

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Speed and VelocitySpeed and Velocity

What is speed, velocity and acceleration?

Speed and VelocitySpeed and Velocity

(Use with Speed, Velocity and Acceleration handout)

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Speed (s) = distance (d)time (t)

Speed is the distance traveled per unit of time.

Each variable measured by units:

Distance: meters (m), miles (mi)

Time:seconds (s), hours (hr), minutes (min)Speed: meters per second (m/s),

miles per hour (mi/hr), kilometers per hour (km/hr)

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Pretend you are looking at your car's speedometer while you are driving. The reading you get from your

speedometer is

This is the speed that you are traveling at that moment.

A. instantaneous speed…

3 TYPES OF SPEED

Instantaneous, Average, Constant

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C. Average speed is the total distance traveled divided by the total time. It can be calculated using the following formula:

speed =distance

time

...or shortened:

Average Speed is:

Total distance = all distance traveled

over

Total time =

final time (end) minus initial time (beginning)

B. Constant Speed is when the object covers equal distances in equal amounts of time.

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Four Step Approach to Solving ProblemsG.U.E.S.S.A.

Step 1 READ THE PROBLEM. Draw a picture.

Step 2 IDENTIFY THE VARIABLESWrite down what you know. GIVENWhat are you trying to find?

UNKNOWN

Step 4 PLUG IN THE NUMBERS. SUBSTITUTE

DO THE MATH SOLVE. Check ANSWER with UNITS

Step 3 WRITE FORMULA EQUATION

Set up the formula. (The formula should match the

unknown.)

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“A car traveled 110 miles in 2 hours.”

Consider the problem…

d =t =s =

Formula Plug-in Answer

Units, units, units!

Step 1 Read the problem.Draw a picture.

110 miles2 hours

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“A car traveled 110 miles in 2 hours.”

d =t =s =

Formula Plug-in Answer

Units, units, units!

110 miles2 hours

Step 2 Write down what you know. GIVEN What are you trying to find? UNKNOWN

110 miles2 hours

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“A car traveled 110 miles in 2 hours.”

d =t =s =

Formula Plug-in Answer

Units, units, units!

110 miles2 hours

Step 3 Set up the formula. FORMULA SHOULD MATCH THE UNKNOWN

s =d

t

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“A car traveled 110 miles in 2 hours.”

d =t =s =

Formula Plug-in Answer

Units, units, units!

110 miles2 hours

Step 3 Set up the formula. EQUATION

dt

S =

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“A car traveled 110 miles in 2 hours.”

d =t =s =

Formula Plug-in Answer

Units, units, units!

110 mi2 hours

Step 4 Plug-in the numbers. SUBSTITUTE

AND SOLVE. CHECK UNITS

dt

110 mi2 hr 55 mi/hr55mi/hr

55 mi/hr

S = S = S =

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Do the problems 1-3 on your notes.

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“A runner’s average speed during the 10 kilometer race was 20 km/hr. What was his time?’”

Consider the problem…

d =t =s =

Formula Plug-in Answer

Units, units, units!

Step 1 Read the problem.

Draw a picture.

10 kmSpeed of runner:

20 km/hr

CIRCLE AND LABEL INFO PROVIDED!

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d =

t =s =

Formula Plug-in Answer

Units, units, units!

10 km

20 km/hr

Step 2 Write down what you know. GIVEN What are you trying to find?

UNKNOWN

10 kmSpeed of runner:

20 km/hr

“A runner’s average speed during the 10 kilometer race was 20 km/hr. What was his time?”

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Formula Plug-in Answer

Units, units, units!

Step 3 Set up the formula. FORMULA MUST MATCH UNKNOWN

“A runner’s average speed during the 10 kilometer race was 20 km/hr. What was his time?’”

d =

t =s =

10 km

20 km/hr

t = d

s

t (hr) = d (km)

s (km/hr)

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Formula Plug-in Answer

Units, units, units!

Step 4 SUBSTITUTE AND SOLVEPlug-in the numbers and do the math.Check units for answer.

10 km

20 km/hr

d =

t =s =

10 km

20 km/hr

0.5 hr

“A runner’s average speed during the 10 kilometer race was 20 km/hr. What was his time?’”

Time: 0.5 Hour

t = d

st

(hr)

= =0.5 hr

10 km

20 km/hr

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Do the problems 4-5 on your notes.

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“You decide to go to Dallas to see friends. Your friends tell you that it takes 4 hours to get to Dallas at an average speed of 70 miles per hour. Approximately how many miles is it to their house?”Step 1 Read the problem.

Draw a picture.

Step 2 Write down what you know. GIVENWhat are you trying to find? UNKNOWN

Step 4 Plug-in the numbers. SUBSTITUTEDo the math. SOLVE. ANSWER with correct

unit.

Step 3 Set up the formula. EQUATION

Formula Plug-in Answer

Units, units, units!

d =

t =s =

280 mi

70 mi/hr

4 hr

?

70 miles per hour

d = s * t= 280 mid =70 mi/hr * 4 hr

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Do problem 6 on your notes.

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Instantaneous speed (Reading on your speedometer)

and Average speed (Total distance traveled over

total time)

Both do not involve direction.

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What is the difference between speed and

velocity?

55 mi/hr

55 mi/h

r

55 mi/hr

All of these cars had different velocities

because they were traveling in different directions.

Velocity has speed & direction.

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Rate of Swimmers

0

400

800

1200

1600

2000

2400

0 5 10 15 20 25 30

Time in minutes

Dis

tanc

e in

met

ers

A distance/time graph makes it possible to “see” speed.This graph shows how fast the swimmers went during their workout.

Which swimmer swam at a constant (the same) speed throughout her workout?

Which one stopped during his/her workout?

Consta

nt spee

d

Stopped here

400 meters at 10, 15, & 20 minutes

Is a

str

aight l

ine

A distance/time graph makes it possible to “see” speed.This graph shows how fast the swimmers went during their workout.

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Make the speed graph& answer the questions.

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Acceleration

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This brings up an important point. In common language,

when things speed up, we say that they are "accelerating,"

and, when they slow down, we say that they are "decelerating."

Any time an object's velocity is changing, we say that the

object is accelerating.

Acceleration is defined as the

change in velocity over time.

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However, in the language of physics, we say that

both objects are accelerating, not because both objects are speeding

up, but because both objects have changing

velocities.

•POSITIVE ACCELERATION (SPEEDING UP)

* NEGATIVE ACCELERATION (DECELERATING) SLOW DOWN

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Acceleration is defined as the

change in velocity over time.

(change) in velocity

timeacceleration =

final velocity – initial velocity

timeacceleration =

Vf - Vi

ta =

27 A go-cart started from the top of a hill at 5 meters per second. At the bottom of the hill it ended up with a speed of 35 meters per second 6 seconds later. What was the acceleration of the go-cart?

Step 1 Read the problem. Draw a picture.

top

bottom35 m/s

5 m/s

In 6 sVf =

Vi=

t =

a =

Formula Plug-in Answer

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top

bottom35 m/s

5 m/s

6 sVf =

Vi=

t =

a =

Formula Plug-in Answer

Step 2 Write down what you know. What are you trying to find?

35 m/s

5 m/s

6 s

Finish:final

Velocity

Start:initial

Velocity

final velocity – initial velocitytimeacceleration =

A go-cart started from the top of a hill at 5 meters per second. At the bottom of the hill it ended up with a speed of 35 meters per second 6 seconds later. What was the acceleration of the go-cart?

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top

bottom35 m/s

5 m/s

6 sVf =

Vi=

t =

a =

35 m/s

5 m/s

6 s

Final Velocity

InitialVelocity

Step 3 Set up the formula.

Formula Plug-in

Vf - Vi

t

Answer

Vf - Vi

t

A go-cart started from the top of a hill at 5 meters per second. At the bottom of the hill it ended up with a speed of 35 meters per second 6 seconds later. What was the acceleration of the go-cart?

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Vf =

Vi=

t =

a =

Formula Plug-in Answer35 m/s

5 m/s

6 s

Vf - Vi

t

35m/s – 5 m/s

6s

30 m/s

6 s= 5 m/s2

Step 4 Plug-in the numbers.Solve.

5 m/s2

A go-cart started from the top of a hill at 5 meters per second. At the bottom of the hill it ended up with a speed of 35 meters per second 6 seconds later. What was the acceleration of the go-cart?

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5 m/sec2

• 5 m/sec increase in speed every second.• 0 sec 0 m/sec• 1 sec 5 m/sec• 2 sec 10 m/sec• 3 sec 15 m/sec• 4 sec 20 m/sec• 5 sec 25 m/sec• 6 sec 30 m/sec

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Do the problems 8-9 on your notes.

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Velocity involves both speed and direction. Changing velocity does not have to necessarily involve a change in speed. It could just involve a change in direction.7

0 m

i/h

70 mi/h

70 mi/h

70 m

i/h

70 mi/h

70 mi/h

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Constant Speed Constant Speed of 55 mphof 55 mph

1. Consider a car moving at a constant speed of 55 mph while turning in a circle.

2. The car's velocity is not constant, even though the speed is constant.

3. WHY? This is because the direction of motion is constantly changing while the car is turning around the track.

4. Since the direction is changing, even though the speed is not, the velocity is changing (velocity involves both speed and direction).

Think Differently About AccelerationThink Differently About Acceleration

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Constant Speed Constant Speed of 55 mphof 55 mph 6. As a result, the car is accelerating,

even though it is neither speeding up nor slowing down.

5. The car is accelerating because its velocity is changing.

Think Differently About AccelerationThink Differently About Acceleration

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Speed of Sound

• If you shout at a wall that is 40 meters away how long will it take before you hear the echo of your voice. (The speed of sound = 343 m/sec)

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Speed of Sound

• If you shout at a wall that is 40 meters away how long will it take before you hear the echo of your voice. (The speed of sound = 343 m/sec)

• V = D 343 = 80 343T = 80 T T 343 343

T = .23 seconds

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Speed of Sound

• A lightening bolt flashes in the distance and 5 seconds later you hear the clash of thunder. How far away was the lightening? (Speed of sounds = 343 m/sec)

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Speed of Sound

• A lightening bolt flashes in the distance and 5 seconds later you hear the clash of thunder. How far away was the lightening? (Speed of sounds = 343 m/sec)

• V = D 343 = D D = 1715 m

T 5

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Speed of Light

• Light from the sun is traveling at a speed of 186,000 miles/sec. It takes light 8 minutes to reach the Earth. Calculate the distance from the Earth to the sun.

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Speed of Light

• Light from the sun is traveling at a speed of 186,000 miles/sec. It takes light 8 minutes to reach the Earth. Calculate the distance from the Earth to the sun.

• V = D 186,000 = D T 480D = 89,280,000 miles