One Dimensional Motion Distance and Displacement Speed and Velocity Graphing Speed/Velocity Acceleration Free Fall.

One Dimensional Motion

Distance and Displacement

Speed and Velocity

Graphing Speed/Velocity

Acceleration

Free Fall

Question of the Day…

Match each unit on the right with the type of measurement with which it would most likely be used.

1. Diameter of a Hydrogen atom a. Light-year

2. Distance from the Sun to Earth b. nanometer

3. Wavelength of a photon of visible light c. angstrom

4. Distance from our sun to the nearest star d. micron

5. Diameter of a red blood cell e. Astronomical unit

The Answers…..

1. C

2. E

3. B

4. A

5. D

Choosing a Frame of Reference

Before describing the motion of an object, you need to have a frame of reference.

A frame of reference is a system of objects that are not moving relative (compared) to one another.

The earth is a common frame of reference.

Motion

Motion is the change in the position of an object.

When this change is compared to another object, it is called relative motion. The reference object can be either at rest or in motion.

Linear motion is motion in a straight line.

Measuring Distance

Distance is the length of a path between two points.

When an object moves in a straight line, the distance is the length of the line connecting the object’s starting and ending points.

Example: Walk 5 meters, then walk 10 meters.

Measuring Displacements

Displacement is the direction from the starting point and the length of the straight line from the starting point to the ending point.

Displacement is distance with a specific direction.

Example: Walk 5 miles north, then walk 10 miles southeast.

See an example of distance vs. displacement

Distance vs. Displacement

Combining Displacements

Displacements are added using vectors. A vector is a measurement that has a

magnitude (number) and a direction. When two things occur in the same direction,

the vectors add. When they act in opposite directions, they

subtract. When added (or subtracted), the sum (or

difference) is called the resultant vector.

Combining Displacements

Start5 m 7 m 10 m

Return to Home Page

Question of the day…Quiz (10 pts)

Please place all answers on a separate sheet of paper.

1. A student walks 3 blocks from his home to school, walks home for lunch, and then returns to school. What is (a) the total distance he walked, and (b) his overall displacement.

2. To get to a friends house, you make the following trip: 5 blocks north, 7 blocks west, and 5 blocks south. (A) What distance did you travel? (B) how far away is your friends’ house?…include distance AND direction!

Speed

Speed can be defined in a couple of ways:

How fast something is moving

The distance covered in a certain amount of time

The rate of change of the position of an object

Units for speed are: miles / hour (mi/hr)

kilometers / hour (km/hr)

feet / second (ft/s)

This is the standard unit meters / second (m/s)

Average and Instantaneous Speed

total distance covered

time to travel that distance

Instantaneous Speed is the speed at any instant in time.

Average Speed =

During a typical trip to school, your car will undergo a series of changes in its speed. If you were to inspect the speedometer readings at regular intervals, you would notice that it changes often. The speedometer of a car reveals information about the instantaneous speed of your car; that is, it shows your speed at a particular instant in time.

For each use of velocity described below, identify whether it is instantaneous velocity or average velocity.

1. The speedometer on your car indicates you are going 65 mph

2. A race-car driver was listed as driving 120 mph for the entire race.

3. A freely falling object has a speed of 19.6 m/s after 2 seconds of fall in a vacuum.

4. The speed limit sign says 45 mph.

Calculating Speed

t

dvspeed

time

distance

V

d

t

Example

Sound travels at a speed of 330 m/s. If a firecracker explodes 3630 m away from you, how long does it take for the sound of the explosion to reach you?

Speed, v = 330 m/s distance, d = 3630 m time, t = ?

So it takes 11 seconds for the sound of the explosion to reach you.

ssm

m

v

dt

v

dt

t

dv becomes

11330

3630

:Rearranged

Velocity

Velocity is speed in a particular direction.– 60 m/s north

Constant Velocity does not change in speed or direction.

Changing velocity can be a change in speed, direction, or both. Whenever there is a change in the velocity of an object, that object is said to be accelerating.

Question of the Day…Velocity Quiz

1. If you are driving at 25 m/s and look out the window for 2.5 seconds, what distance have you traveled while looking out the window? (4 pts)

2. To get from the gym to class, you walk a distance of 135 meters. If you walk at a speed of .65 m/s, will you get to class in 4 minutes? (6 pts)

Graphing Speed or Velocity

When constructing a graph of speed or velocity, distance is plotted on the vertical, or y-axis, and time is plotted on the horizontal, or x-axis.

The speed of an object can be found from the graph by calculating the slope of the line.

xinchange

yinchangeslope

Constant Speed Graph

A distance-time graph for constant speed is a straight line.

Speed of a Walking Person

0

2

4

6

8

10

0 5 10 15 20

Time (s)

Dis

tanc

e (m

)

Time (s)

Linear (Time (s))

How far did the person walk in 11 seconds?

What is her average

speed?

What is her instantaneous speed at 8 seconds?

Variable Speed Graph

Speed of a Walking Person

0

2

4

6

8

10

12

14

0 2 4 6 8 10

Time (s)

Dist

ance

(m)

How far did the person walk in 5 seconds?

What is her

average speed?

What is her instantaneous speed at 5.5 seconds? At 7 seconds?

When is she walking faster - from 0-4 seconds or from 6-8 seconds?

Return to Home Page

Question of the Day….Quiz (10 pts)

1. A car travels 1200 m in 2 minutes. What is its average velocity in m/s? (3 pts)

2. A sprinter runs 10 m in 30 seconds, then speeds up to 1 m/s for 1 minute.

a) What is her average speed for the whole trip? (2 pts)

b) What is her instantaneous speed at 45 sec? (2 pts)

c) Make a distance vs. time graph for this example (3 pts)

Question of the Day…Acceleration

Write each of the following in your notebook. Circle each situation described below in which the object has an acceleration. For each one you circle, identify the direction in which the acceleration is acting.

1. A car moves to the right while slowing down.

2. A marble moves in a circular path inside a paper plate at a constant speed.

3. The moon orbits the Earth.

4. An air hockey puck moves smoothly across the air hockey table after being struck.

5. A rocket is launched upward from the launch pad.

Answers….

1. yes, this is deceleration.

2. Yes, this is centripetal acceleration

3. Yes, also centripetal acceleration

4. No, this is constant velocity

5. Yes, this is acceleration

Acceleration

Acceleration is the rate at which velocity changes.

Any time velocity changes, an object is undergoing an acceleration.

A decrease in velocity is called deceleration.

This change can be by speeding up, slowing down, or changing direction.

Acceleration

Units of acceleration are:

(miles / hour) / second mph/s

(kilometers / hour) / second kmh/s

(feet / second) / second ft/s2

This is the standard unit (meters / second) / second m/s2

Acceleration along the ground is horizontal acceleration.

Vertical acceleration is called “free fall”.

Calculating Acceleration

time

velocityinitialvelocityfinalonaccelerati

Example

A car’s velocity at the top of a hill is 10 m/s. Two seconds later it reaches the bottom of the hill with a velocity of 26 m/s. What is the acceleration of the car?

2m/s8onaccelerati

s2

m/s16onaccelerati

s2

m/s10m/s26onaccelerati

time

velocityinitialvelocityfinalonaccelerati

The car is increasing its velocity by 8 m/s for every second it is moving.

Graphing Acceleration

A velocity vs. time graph is used to find acceleration.

What is the final velocity of the car?

What is the instantaneous velocity of the car at 3 seconds?

What is the acceleration of the car?

Acceleration of a Car

0

5

10

15

20

25

30

35

0 2 4 6 8

Time (s)

Vel

oci

ty (

m/s

)

Return to Home Page

Free Fall

The acceleration of a falling object is due to the force of gravity between the object and the earth.

Galileo showed that falling objects accelerate equally, neglecting air resistance.

On the surface of the earth, in a vacuum, all objects accelerate towards the surface of the earth at 9.8 m/s2. This value is called “g”.

Effect of Gravity on an Object

Without Air resistance With Air resistance

Gravity and an Accelerating Object

Since the acceleration of gravity is 9.8 m/s2, an object increases (or decreases) its velocity by 9.8 m/s each second.

Free Fall Velocity for a dropped object

0

10

20

30

40

50

60

70

0 2 4 6 8

Time (s)

Vel

oci

ty (

m/s

)

What is the speed of the object after 3 seconds? After 5 seconds?

What is the acceleration of the dropped object after 2 seconds? After 6 seconds?

How would this graph change if the object were thrown up into the air?

Question of the Day…Quiz (10 pts)

Description of Motion Direction of Velocity Direction of Acceleration

A ball is dropped from a ladder.

A car is moving to the right when the driver applies the brakes to slow down.

A ball is tied to a string and being swung clockwise is at the top of its circular path.

A sled is pushed to the left causing it to speed up.

Complete the table below by drawing arrows to indicate the directions of the object’s velocity and acceleration (remember it’s not always up and down).