TOPIC I.

I.

• Branch of Mechanics that deals with motion without regard to forces producing it.

A. Distance and Displacement1. Distance: the total length of the path that an object travels.

a. A scalar quantityb. SI Unit is the meter (m)c. length, width, and height

are all distances!

2. Displacement: the change in position of an object.

a. A vector quantity because it has a both magnitude and direction

b. “As the crow flies” (magnitude is a straight line from initial to final

positions)

A B

C

Displacement Look!!!

A Right Triangle!!!

c. SI unit for displacement is the meter (same as for distance)

d. magnitudes for displacement and distance are NOT usually the same!

10 m

7 m

7 m10 m

10 m • What is the

distance traveled?

Start

End

44 m

Example: Displacement

• What is the displacement?

10 m

7 m

7 m10 m

Start

End A Right Triangle has

been formed!

Use the Pythagorean Theorem!

(10 m)2 + (14 m)2 = c2100 m2 + 196 m2 = c2296 m2 = c2

17.2 m = c

10 m

B. Speed and Velocity1. Speed: the distance an object moves

per unit timea. Speed is a scalar quantity b. SI units are meters per second

(m/s)c. other units for speed:

• kilometers per hour (km/hr or kph)

d. Formula for average speed (v):

d = distance (m)

t = time (s)

_

t

dv

Example: Speed Conversion!

If you were traveling 170 km/hr, what is your speed in meters per second (m/s)?

Answer: 47.2 m/s

What is this speed in MPH? Would you get a ticket?

Answer: 105.6 mph

YES!!

2. Velocity: the time rate of change of an object’s displacement

a. A vector quantity since it adds direction to speed

b. Units: (m/s) but with a direction attached

c. It is possible that two objects can have the same speed, but different velocities

+ = velocity

d. Finding Velocity Mathematically (using formulas)

1. Basic formula:

Reference Tables!!

2. Also:

t

dv

2fi vv

v

f

i

v

v

t

d

v average velocity

displacement

time

initial velocity

final velocity

Examples: Velocity

What is the average velocity of a car that travels 2450 meters to the east in 1 minute?

How long does it take a jet to fly 1 kilometer if its velocity is 250 m/s North?

C. Acceleration1. Definition: is the rate of change of velocity.

• “how fast something is speeding up or slowing down”

• Example: gas pedal = increasing speed

(accelerator)

2. Acceleration is a vector quantity! Always has a direction attached!

3. Formula:

t

va

timet

velocityinchangev

onacceleratia

4. Units for acceleration using dimensional analysis:

t

dv

t

va

ssm

2s

m

s

m

5. Finding Acceleration Mathematicallya. Basic formula for “change in

velocity per unit time”:

• since Δv = vf – vi

substitute into the above equation:

t

Δva

t

vva if

• solve for final and initial velocities:

atvv if

atvv fi Speed

(m/s

)

Time (sec)

iv

fva

t

Example: Acceleration

The space shuttle starts from rest and speeds up to 10000 kilometers per hour in 90 seconds. What is the acceleration of the shuttle?

A truck speeds up at a rate of 10 m/s2. If the truck was initially travelling 15 m/s, how fast would it be travelling after 20 seconds?

b. Acceleration with displacement or distance (d):

• Now d can be expressed as:

2

2

1attvd i

Example: Solve for a

Example: Find Displacement

A car decelerates rapidly from 26.94 m/s and comes to rest in 3.25 s. The deceleration provided by the brakes is 8.3 m/s2. How far does the car travel while stopping? Assume the car was traveling South.

Warm Up #6 //14

A school bus slowly drives through Carrollton at 35 mi/hr.

What is the bus speed in meters per second?

What how far will the bus travel in 10 seconds?

What is the acceleration of the bus if it comes to a stop in 5 seconds?

Example: Find a

In a drag race, two beat up, old, Honda Civics with need to cover 500 meters. The cars start from rest and reach top speed in 8 seconds. What is the acceleration of the cars?

advv if 222

d. Bottom Line:

any piece of unknown information can be found if 3 variables in any situation are known:d, vi , vf , t , and a

c. If time is NOT known:

Example: Find Final Velocity

A car accelerates from 10 m/s at a rate of 5 m/s2 over the course of 100 meters. What is the car’s final velocity? Assume the car was traveling West.

Example: Find Distance

A sled moving at 5 m/s decelerates to rest at a rate of 2 m/s2. How far did the sled travel while it was coming to a stop?

e. Many times, objects start from rest, causing initial velocity (vi) to be zero!

• This makes equations easier!

t

va f

t

vva if

2fi vv

v

2fv

v 2

2

1attvd i

2

2

1atd

advv if 222

adv f 22

D. Graphing Motion1. Distance vs. Time

a. Constant Speed

Time

Dis

tan

ce

Positive Direction

Negative Direction

b. Changing Speed (acceleration)

Time

Dis

tan

ce

Increasing Speed

Time

Decreasing Speed D

ista

nc

e

c. No Movement

Dis

tan

ce

Time

2. Speed Versus Time Graphs

Speed

(m/s

)

Time (sec)

a. Constant or Uniform Acceleration

(speed is increasing at a steady rate)

Speeding UP!!

Speed

(m/s

)

Time (sec)

b. Constant or Uniform Deceleration

(speed is decreasing at a steady rate)

Slowing DOWN!!

Speed vs. Time

NEGATIVE Acceleration

Speed

(m/s

)

Time (sec)

Speed vs. Time

c. NO Acceleration: Velocity is constant!

Steady Speed!

3. Slopes of Motion Graphs

run

riseslope

x

yslope

or

Practice:

• Calculate the slope of the graph… (units!)• What was the velocity at 2.5 seconds?• What time was the object moving at

25m/s?• What does the slope of the graph mean?

4. Positive and Negative Motion Graphs

D. Freely Falling Objects1. In a space all objects will fall or accelerate toward the most dominant source of gravity (usually a large mass).

2. Earth causes falling objects accelerate at a constant 9.81m/s2 toward the planet’s center.

symbol g

4. ALL Free falling objects are instantaneously accelerated or decelerated at a rate of g the moment they are released

3. The equations for motion are usable in the cases of freely falling objects: replace a with g.

2

2

1gttvd i gtvv if gdvv if 222

• note what happens to these equations when an object is dropped “from rest”

Cat