Linear motion
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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

Linear Motion

Edison Business

Mr. Marrero


What is kinematics

What is kinematics?

  • Branch of physics that describes the motion of objects


Think of your lab

Think of your lab


Average speed

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


Another way

Average speed

v = average speed

vi = initial speed

vf = final speed

Another Way


Think of motion grab a white board

Think of motion (Grab a white board)

D

D

T

T


Think of motion

Think of motion

D

D

T

T


Explain how this person is moving

Explain how this person is moving


Think again typical problem

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

Think again – Typical Problem


Think again typical problem1

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

Think again – Typical Problem


Think again typical problem2

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

Think again – Typical Problem


Practice

Practice


Bellwork

Bellwork

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


Speed vs time graphs

Speed Vs Time Graphs

Slope

Speed (m/s)

Area under curve

Time (s)


Acceleration

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

Acceleration


What s happening

What’s happening?

Speed (m/s)

Speed (m/s)

Time (s)

Time (s)


What s happening1

What’s happening?

Speed (m/s)

Speed (m/s)

Time (s)

Time (s)


Typical problems

Typical problems

  • Find the acceleration of the object


Typical problems1

Typical problems

  • Find the total distance traveled by the object


Linear motion

  • Find the acceleration of the object the first second.

  • Find the distance traveled during this time.


Linear motion

  • Find the acceleration between 1 and 2 seconds.

  • Find the distance traveled during this time.


Linear motion

  • Find the acceleration between 3 and 4 seconds.

  • Find the distance traveled during this time.


Linear motion

  • Find the acceleration between 5 and 6 seconds.

  • Find the distance traveled during this time.


Linear motion

  • Find the acceleration between 6 and 8 seconds.

  • Find the distance traveled during this time.


Linear motion

  • Find the acceleration between 8 and 10 seconds.

  • Find the distance traveled during this time.


Practice1

Practice


To solve physics problems

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 speed1

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

Typical Problem

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


Use the steps

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

Use the steps


Example 2

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

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

Example # 4

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


Acceleration1

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

Acceleration


Example

Example:

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


Example1

Example

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


Acceleration rewritten

Solve for Vf

Vf = Vi + at

Acceleration rewritten!!


Example2

Example:

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


Example3

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 v f

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


Example4

Example:

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


Independent of time

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


Example5

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?


Practice2

Practice


Free fall

Free Fall

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


Gravitational acceleration

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)


Example6

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?


Example7

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?


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