One Dimensional Motion Physics I 1 kg1000 g 1 g1000 mg 1 m1000 mm 1 m100 cm 1 cm10 mm 1 min60 sec 1...

One Dimensional MotionPhysics I

1 kg 1000 g

1 g 1000 mg

1 m 1000 mm

1 m 100 cm

1 cm 10 mm

1 min 60 sec

1 hour 3600 sec

1 L 1000 mL

Metric Conversions YOU must know.

Speed and VelocitySpeed and Velocity

MHS PhysicsMHS Physics

Magnitude

• Size

Scalars (Magnitude)

Vector (Magnitude and Direction)

Distance (20 m) Displacement (20 m, North or +20 m)

Speed (20 m/s) Velocity (20 m/s, North or +20 m/s)

Mass (20 kg) Acceleration (+20 m/s2)

Time (20 seconds)

Scalar – Quantity with magnitude only

Vector – Quantity with magnitude and direction

Distance vs. Displacement

Displacement can be negative!

Distance

Displacement or change in position

Initial position, xo

Final position, x

(x-xo=x)

Cutnell & Johnson

Distance vs. DisplacementDistance vs. Displacement

Distance and Displacement• For motion along x or y axis, the displacement is determined

by the x or y coordinate of its final position. Example: Consider a car that travels 8 m, E then 12 m, W.

• For motion along x or y axis, the displacement is determined by the x or y coordinate of its final position. Example: Consider a car that travels 8 m, E then 12 m, W.

Net displacement D is from the origin to the final position:

What is the distance traveled? 20 m !!

12 m,W

D

D = 4 m, WD = 4 m, W

x8 m,E

x = +8

Author: Tippens, P. (2007)

Definition of Speed

• Speed is the distance traveled per unit of time (a scalar quantity).

• Speed is the distance traveled per unit of time (a scalar quantity).

s = = dt

20 m 4 s

v = 5 m/sv = 5 m/s

Not direction dependent!

A

Bd = 20 m

Time t = 4 sAuthor: Tippens, P. (2007)

Definition of Velocity

• Velocity is the displacement per unit of time. (A vector quantity.)

• Velocity is the displacement per unit of time. (A vector quantity.)

v = 3 m/s Eastv = 3 m/s East

Direction required!

A

Bd = 20 m

Time t = 4 s

x=12 m

s

m

t

xxv

of

4

12


North

East

Constant Speed

Ticker Tape Diagrams:

Which diagram represents a faster constant speed?

What is the difference in the car’s average velocity in part a) and part b)?

Average velocity Average Speed = t

xv

time

tan

Total

cedisTotal

Cutnell & Johnson

t = 4.740 s

Means change in, so subtract!

Example 1. A runner runs 200 m, east, then changes direction and runs 300 m, west. If the

entire trip takes 60 s, what is the average speed and what is the average velocity?

Recall that average speed is a function only of total distance and total time:

Total distance: s = 200 m + 300 m = 500 m

Avg. speed 8.33 m/s

start

s1 = 200 ms2 = 300 m

s

m

total

TotalAvgSpeed

60

500

time

distance


Example 1 (Cont.) Now we find the average velocity, which is the net displacement divided by

time. In this case, the direction matters.

xo = 0

t = 60 s

x1= +200 mxf = -100 m

x0 = 0 m; xf = -100 m

Direction of final displacement is to the left as shown.

Average velocity: 1.67 m/s, Westv

Note: Average velocity is directed to the west.

t

xv

sms

mmv /67.1

60

0100


Example 2. A sky diver jumps and falls for 625 m in 14 s. After chute opens, he falls another 356 m

in 142 s. What is average speed for entire fall?

625 m

356 m

14 s

142 s

A

B6.10 m/sv 6.10 m/sv

Average speed is a function only of total distance traveled and the total time required.

Average speed is a function only of total distance traveled and the total time required.

Total distance/ total time::


Average velocity Average Speed = t

xv

time

tan

Total

cedisTotal

From a Graphical View: When finding the average velocity for each interval, what feature of the graph are you calculating? (Math term)

Cutnell & Johnson

Position vs. time

-10

-5

0

5

10

15

20

0 10 20 30 40 50 60

Time (s)

Po

sit

ion

(m

)

Interpret the motion of the object in the graph below.

1. How fast (average velocity) is the object traveling in each interval of time? How can this be determined?

2. What is the average velocity of the entire trip?

3. What is the average speed of the entire trip?

During which time intervals did it travel in a positive direction?

During which time interval did it travel in a negative direction?

0-10 sec, 40-55 sec

15-40 sec

+ -

-+

Notice the correlation between the signs of the slopes and the direction it is traveling in each time interval

+

Average Speed and Instantaneous Velocity

The instantaneous velocity is the magnitude and direction of the speed at a particular instant. (v at point C)

The instantaneous velocity is the magnitude and direction of the speed at a particular instant. (v at point C)

The average speed depends ONLY on the distance traveled and the time required.

The average speed depends ONLY on the distance traveled and the time required.

A

Bs = 20 m

Time t = 4 s

C


What direction (pos. or neg.) is the object traveling during 0-1 sec?

When is the object traveling in a neg. direction?

What is the object doing during the 1-2 second interval?

What is the average speed from 2-3 seconds?

What is the instantaneous speed at 3.5 seconds?

Velocity vs. time graph

Positive Velocity indicates positive displacement

1 2 3 4

5

-3

s

m/s2

Average Acceleration

The rate of change in instantaneous velocity, either magnitude, direction, or both.

Acceleration can be either be positive or negative – vector quantity

of

of

tt

vva

Three Ways to Accelerate

t

vva of

Hewitt, P. Conceptual Physics.

Positive and Negative Acceleration

+a

-a

Average Acceleration is a change in velocity over time

Cutnell & Johnson

Positive and Negative Acceleration

x0x

-a

x0x

+a

v0

v0

v

v

Example 3 (No change in direction): A constant force changes the speed of a car from 8 m/s to 20 m/s in 4

s. What is average acceleration?

Step 1. Draw a rough sketch. Step 2. Choose a positive direction (right).

Step 3. Label given info with + and - signs.

+

v1 = +8 m/s

t = 4 s

v2 = +20 m/s


Example 3 (Continued): What is average acceleration of car?

Step 4. Recall definition of

average acceleration.

2 1

2 1avg

v v va

t t t

2 1

2 1avg

v v va

t t t

3 m/s, rightwarda

+

v1 = +8 m/s

t = 4 s

v2 = +20 m/s


2

Example 4: A wagon moving east at 20 m/s encounters a very strong head-wind, causing it to

change directions. After 5 s, it is traveling west at 5 m/s. What is the average acceleration? (Be careful

of signs.)

Step 1. Draw a rough sketch.

+

Step 2. Choose the eastward direction as positive.

vo = +20 m/s vf = -5 m/s

Step 3. Label given info with + and - signs.Author: Tippens, P. (2007)

Example 4 (Cont.): Wagon moving east at 20 m/s encounters a head-wind, causing it to change directions. Five seconds later, it is traveling west at 5 m/s. What is

the average acceleration?

Choose the eastward direction as positive.Initial velocity, vo = +20 m/s, east (+)Final velocity, vf = -5 m/s, west (-)The change in velocity, v = vf - v0

v = (-5 m/s) - (+20 m/s) = -25 m/s

Choose the eastward direction as positive.Initial velocity, vo = +20 m/s, east (+)Final velocity, vf = -5 m/s, west (-)The change in velocity, v = vf - v0

v = (-5 m/s) - (+20 m/s) = -25 m/s


Example 4: (Continued)

aavg = =vt

vf - vo

tf - to

a =-25 m/s 5 s

a = - 5 m/s2 a = - 5 m/s2

+

vo = +20 m/s vf = -5 m/s

East

v = (-5 m/s) - (+20 m/s) = -25 m/s


A student walks 3 meters, North and then 4 meters, South in 6 seconds. What is the

average velocity?

1 2 3 4

45%

36%

0%

18%

1. 1.167 m/s, North

2. 1.167 m/s, South

3. 0.167 m/s, North

4. 0.167 m/s, South

The sign of the velocity of an object represents the

1 2 3 4

15%

23%

8%

54%

1. The magnitude

2. The direction

3. The acceleration

4. The speed

Corresponding Position vs. Time Graph

Corresponding Acceleration vs. Time Graph

What is the instantaneous speed of the object at point B?

1 2 3 4 5

0%

25%

8%

0%

67%

1. 0

2. -2 m/s

3. +2 m/s

4. -1.3 m/s

5. +1.3 m/s

1. When was he traveling in a positive direction?2. When was he traveling in a negative direction?3. When was he at rest?4. During what time intervals did he travel at a constant velocity?5. During what time interval did he travel the greatest distance?

6. When does he have a positive acceleration?

7. When is he increasing his speed? Decreasing his speed?

8. What is the average acceleration during interval A?

9. What is the instantaneous acceleration at 2.5 seconds?

Velocity vs. Time Graphs

AB

CED

F

G

H

Describe the motion of the object.

Initial position is 0.0 m.

5.0

Summary:

Corresponding Shapes of Motion Graphs with Constant Acceleration

d v d v

d v d v

Which graph best matches the statement?

Graph Shapes

Linear; y = mx +b Quadratic: y = x2

Inverse: y = 1/x Inverse Square : y = 1/x2

Credits:

Cutnell & Johnson Physics. (2004). [Text Art CD]. John Wiley & Sons.

Foxtrot Cartoon: Bill Amend. Received from 2007 AP Conference.

Hewitt, P. [Illustrations]. Conceptual Physics.

Nave, R. (2010). Hyperphysics.[Illustration]. Permission granted to use illustrations. Retrieved from

http://hyperphysics.phyastr.gsu.edu/hbase/hframe.html

Tippens, P. (2007). Chapter 6A Acceleration [PowerPoint Slides]. Received from 2007 AP Conference.

One Dimensional Motion Physics I 1 kg1000 g 1 g1000 mg 1 m1000 mm 1 m100 cm 1 cm10 mm 1 min60 sec 1...

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