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# Linear Motion - PowerPoint PPT Presentation

Linear Motion. Edison Business Mr. Marrero. What is kinematics?. Branch of physics that describes the motion of objects. Think of your lab. Average Speed. Definition - Distance covered in a period of time : Equation – v = average speed - (m/s) – meters per second

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Linear Motion

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## Linear Motion

Mr. Marrero

### What is kinematics?

• Branch of physics that describes the motion of objects

### Average Speed

• Definition - Distance covered in a period of time:

• Equation –

• v = average speed - (m/s) – meters per second

• d = distance covered (m) – meters

• t = time (s) - seconds

Average speed

v = average speed

vi = initial speed

vf = final speed

D

D

T

T

D

D

T

T

### Explain how this person is moving

Calculate the average speed of the object during the first 2 seconds

### Think again – Typical Problem

Calculate the average speed of the object between 2 seconds and 4 seconds

### Think again – Typical Problem

Calculate the average speed of the object between 4 seconds and 8 seconds

## Practice

### Bellwork

• Explain how you think the object in the following Velocity (speed) vs time graph is moving

### Speed Vs Time Graphs

Slope

Speed (m/s)

Area under curve

Time (s)

a = D V = Vf - Vi

D t t

Definition – Rate of change of speed in a period of time.

Equation –

a = acceleration (m/s2) = meters per second2

Vi = initial speed or velocity (m/s) = meters per second

Vf = final speed or velocity (m/s) = meters per second

t = time (s) = seconds

Speed (m/s)

Speed (m/s)

Time (s)

Time (s)

Speed (m/s)

Speed (m/s)

Time (s)

Time (s)

### Typical problems

• Find the acceleration of the object

### Typical problems

• Find the total distance traveled by the object

• Find the acceleration of the object the first second.

• Find the distance traveled during this time.

• Find the acceleration between 1 and 2 seconds.

• Find the distance traveled during this time.

• Find the acceleration between 3 and 4 seconds.

• Find the distance traveled during this time.

• Find the acceleration between 5 and 6 seconds.

• Find the distance traveled during this time.

• Find the acceleration between 6 and 8 seconds.

• Find the distance traveled during this time.

• Find the acceleration between 8 and 10 seconds.

• Find the distance traveled during this time.

## Practice

### To solve physics problems

• Identify known variables with units

• Identify unknown variables

• Identify the proper equation

• “plug in” numbers into equation

• solve for unknown

• round if necessary

### Average Speed

• Definition - Distance covered in a period of time:

• Equation –

• v = average speed - (m/s) – meters per second

• d = distance covered (m) – meters

• t = time (s) - seconds

### Typical Problem

• A race car runs 540 Km in 3 hours. What is the average speed of the car?

Identify known variables

d = 540 km

t = 3 hrs

Identify unknown

v =?

Identify proper equation

Plug in numbers

Solve for unknown

v= 180 km /hr

### Example #2

• A plane takes 2 hours to travel from San Juan P.R. to Orlando FL. If Orlando is 900 Km north of San Juan, What is the average speed of the plane?

### Example #3

• A marathon runner maintains a constant speed of 7 m/s during a 1000 m race. How much time did it take the runner to reach the finish line?

### Example # 4

• What is the distance covered by jaguar after running for 10 seconds after Mr. Marrero at 1000 km/h.

a = D V = Vf - Vi

D t t

Definition – Rate of change of speed in a period of time.

Equation –

a = acceleration (m/s2) = meters per second2

Vi = initial speed or velocity (m/s) = meters per second

Vf = final speed or velocity (m/s) = meters per second

t = time (s) = seconds

### Example:

• A train accelerates from rest to 18 m/s in 6 seconds. What is it’s acceleration?

### Example

A race car decelerates from 30 m/s to 15 m/s in 5 seconds. What is it’s acceleration?

Solve for Vf

Vf = Vi + at

### Example:

• A rocket travels from rest with an acceleration of 10 m/s2. What is the speed of the rocket after 5 seconds?

### Example:

• A ball rolls down a hill with an initial speed of 5 m/s. If the ball rolls with an acceleration of 10 m/s2, how much time does it take for it to reach a speed of 20m/s?

### Independent of Vf

• d = distance or displacement (m)

• Vi = initial speed or velocity (m/s)

• t = time (s)

• a = acceleration (m/s2)

d = Vi t + ½ a t2

### Example:

• A Plane accelerates from rest at 5 m/s2. What is it’s displacement after 10 seconds?

Vi = initial speed or velocity (m/s)

Vf = final speed (m/s)

d = distance (m)

a = acceleration (m/s2)

### Independent of time

• Vf2 = Vi2 + 2 ad

### Example

• A plane needs a speed of 80 m/s to lift off. If the track is 2 x 103m, what must its acceleration be to reach take of speed?

## Practice

### Free Fall

• Free Fall – motion with no acceleration other than that provided by gravity

a = g = 9.81 m/s2

All Falling objects in free fall accelerate at the same rate

REGARDLESS OF THEIR MASS!!!!!!!!!!

For all “free fall” problems’ assume:

### Gravitational Acceleration

• a = acceleration (m/s2)

• g = acceleration due to gravity (m/s2)

### Example:

• A basketball is dropped from the roof of a coliseum.

• a) What is the ball’s speed after 4 seconds?

• b) How tall is the coliseum?

### Example:

• A student drops a stone from a bridge into the river.

• If it takes 25 seconds for the stone to hit the river, how tall is the bridge?

• What is the speed of the rock when it hits the river?