Speed and Velocity

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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 =distance

time

Speed is the distance traveled per unit of time.

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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.

instantaneous speed…

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Average speed is the distance traveled divided by the time. It can be calculated

using the following formula:

speed =distance

time

s =d

t

...or shortened:

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Four Step Approach to Solving Problems

Step 1 Read the problem. Draw a picture.

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

Step 4 Plug-in the numbers.Solve.

Step 3 Set up the formula.

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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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d =t =s =



110 miles2 hours

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

110 miles2 hours

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d =t =s =



110 miles2 hours


s =d

t

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d =t =s =



110 miles2 hours


dt

S =

10


d =t =s =



110 mi2 hours


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 =




10 kmSpeed of runner:

20 km/hr

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d =

t =s =



10 km

20 km/hr


10 kmSpeed of runner:

20 km/hr


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d =

t =s =

10 km

20 km/hr

s = d

t

s (km/hr) = d (km)

t (hr)

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10 km20 km

d =

t =s =

10 km

20 km/hr

.5 hr


Time: 0.5 Hour

S = d

tt (hr)

= 10 km20 km x t (hr)

=1 Hr (t)

Proportion Problem… Cross multiply and divide…

.5 hr

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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.

What are you trying to find?





d =

t =s =

280 mi

70 mi/hr

4 hr

?

70 miles per hour4 hours

s = d / t70 mi/hr = d/4 hr

70 mi1 hr

= d (mi)

4 hr

70mi x 4hrd x 1hr

=280 mi

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Do problem 6 on your notes.

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Instantaneous speed (Reading on your speedometer)

and average speed 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

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Make the speed graph& answer the questions.

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Acceleration

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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 =

25 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?


top

bottom35 m/s

5 m/s

In 6 sVf =

Vi=

t =

a =


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top

bottom35 m/s

5 m/s

6 sVf =

Vi=

t =

a =



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


Formula Plug-in

Vf - Vi

t

Answer

Vf - Vi

t


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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


5 m/s2


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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.

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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

Speed and Velocity

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