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Linear Motion

- Holt Physics, pages 39 - 81

Distinguish displacement from distance

- Distance is a scalar quantity, which means that

is only needs a magnitude. It is how far you are

from a reference point. - Displacement is a vector quantity, which means it

needs both magnitude and direction. It is how

far you ended up from where you started and in

what direction. Therefore, distance is the

magnitude of a displacement vector.

Distinguish displacement from distance (contd)

- For instance, if you leave home and drive from

Houston to Dallas, your displacement is

approximately 200 mi, North. When you return to

Houston at the end of the trip, your displacement

is now zero because you are now back at the place

you started.

Distinguish velocity from speed

- Speed is a scalar quantity. It is how fast you

are traveling. When you look at the speedometer

on your car, it tells you the speed you are

traveling at that moment. - Velocity is a vector quantity. It is how fast

you are going and in what direction. If you are

traveling to Dallas, you may be traveling at 70

mi/hr, North.

Define acceleration

- Acceleration is a vector quantity. It is the

rate at which the velocity is changing. Since

velocity is dependent on either speed or

direction, if either of those change, your

velocity changes and you have acceleration. - Deceleration is a special name given to an

acceleration that is in a direction opposite to

the direction of motion of the object.

Hot Wheels Track

Define frame of reference.

- A frame of reference is necessary to fully

explain motion. It is the position from which

the motion is being observed. - The frame of reference is assumed to be

stationary. - Your frame of reference affects the motion you

perceive.

Give an example of a frame of reference.

- If you are looking at Spring H.S. from across the

street, it appears to be sitting still but if you

were viewing it though a telescope from the moon,

it would appear to be rotating along with the

earth which is turning on its axis.

Define the concept of relativity of velocities.

- Velocity is also affected by the frame of

reference. This is known as relative velocity.

It is the velocity of one object with respect to

another object.

Use the concept of relativity of velocities.

(contd)

- If you are riding on the bus talking to your

friend, his apparent speed is 0 m/s. - However if you are standing on the street corner

and the bus drives by without stopping, his

apparent speed is now 40 mi/hr (the speed of the

bus). - If you are in your moms car going 50 mi/hr when

you pass your friend on the bus that is going 40

mi/hr then your friend appears to be going 10

mi/hr (or 10 mi/hr in the opposite direction).

Define average velocity

- Average velocity is the total change in position

divided by the time interval over which it

occurred.

v average velocity in m/s ?d displacement in

meters ?t time in seconds

Define average velocity (contd)

- If two objects have the same average velocity

means that both objects have the same

displacement in the same time.

Sample Problem

- Suppose a car travels at a constant 10 m/s. How

far would it move in one minute?

Sample Problem

- You drive a car 2 hours at 40 km/h, then 2 hours

at 60 km/h. What is your average velocity? Do

you get the same answer if you drive 100 km at

each of these two speeds?

Answer 50 km/h no, 48 km/h

Average vs. Instantaneous Speed

Plot and interpret position-time graphs

- A position time graph shows an objects change in

position over a period of time.

Plot and interpret position-time graphs

- An object which is not moving would have the same

position over the period of time, so the graph

would be a horizontal line. The y-intercept of

this line indicates the distance of the object

from a stationary reference point.

Plot and interpret position-time graphs (contd)

- An object which is moving at a constant positive

velocity would cover equal distances in equal

amount of time and its graph would appear as an

upwardly sloping diagonal line.

Plot and interpret position-time graphs (contd)

- An object which is moving with a constant

negative velocity would also cover equal

distances in equal amounts of time but its

distance from the reference point would be

decreasing. Its graph would be a downward

sloping diagonal line.

Plot and interpret position-time graphs (contd)

- An object which is moving with a constant

positive acceleration will cover larger and

larger distances in successive equal time

intervals. Its position time graph would appear

as a curve.

Plot and interpret position-time graphs (contd)

- An object which is moving with a constant

negative acceleration will cover smaller and

smaller distances in successive equal time

intervals.

Calculate the velocity of an object from a

position time graph

- The slope of the position time graph is the

velocity of the object.

Calculate the velocity of an object from a

position time graph

Plot and interpret position-time graphs

- The faster an object is moving, the steeper the

line on the position time graph.

Passing Lane DT Graphs

Define instantaneous velocity

- Instantaneous velocity is the velocity at any

instant. - When an object is moving at a constant velocity,

the instantaneous velocity and the average

velocity are ALWAYS the same. - When an object is accelerating, the instantaneous

velocity and the average velocity are NOT the

same at all times.

Define instantaneous velocity (contd)

- To find the instantaneous velocity of an

accelerating object from a position time graph,

you can find the slope of the line that is

tangent to the curve at the point in time for

which you want the instantaneous velocity.

Plot and interpret a velocity-time graph

- An object which is not moving would have no

velocity over the entire period of time, so the

graph would be a horizontal line along the

x-axis.

Plot and interpret a velocity-time graph

- An object which is moving at a constant positive

velocity would maintain the same velocity over

the entire time interval and its graph would

appear as a horizontal line above the x-axis.

The y-intercept indicates the constant velocity

of the object.

Passing Lane VT Graphs

Plot and interpret a velocity-time graph

- An object which is moving at a constant negative

velocity would maintain the same velocity over

the entire time interval and its graph would

appear as a horizontal line below the x-axis.

The y-intercept indicates the constant velocity

of the object.

Plot and interpret a velocity-time graph

- An object which is moving with a constant

positive acceleration will have a velocity time

graph that is an upwardly sloping diagonal line.

The y-intercept is the initial velocity of the

object.

The Stoplight

Plot and interpret a velocity-time graph

- An object which is moving with a constant

negative acceleration will have a velocity time

graph that is an downwardly sloping diagonal

line. The y-intercept is the initial velocity of

the object.

Motion of a Two-Stage Rocket

Calculate the acceleration of an object from a

velocity time graph

- The slope of the velocity time graph is the

acceleration of the object.

Calculate the acceleration of an object from a

velocity time graph

Calculate the displacement from a velocity time

graph

- The area between the velocity time graph and the

x-axis is the displacement of the object during

that time interval.

Sample Problem

- What is the displacement of the object during the

first 5 seconds?

Sample Problem (contd)

Sample Problem (contd)

Sample Problem (contd)

- To find the total displacement of the object

during the 25 seconds, you would break the shape

into easily calculated areas as shown, calculate

the individual areas then add them together.

Plot and interpret an acceleration-time graph

- An object which is not moving would have no

acceleration over the entire period of time, so

the graph would be a horizontal line along the

x-axis.

Plot and interpret an acceleration-time graph

- An object which is moving with either a constant

positive or negative velocity would have no

acceleration over the entire period of time since

the velocity is not changing. So the graph would

be a horizontal line along the x-axis.

Plot and interpret an acceleration-time graph

- An object which is moving with constant positive

acceleration would graph as a horizontal line

above the x-axis. The y-intercept would be equal

to the value of the acceleration.

Plot and interpret an acceleration-time graph

- An object which is moving with constant negative

acceleration would graph as a horizontal line

below the x-axis. The y-intercept would be equal

to the value of the acceleration.

Calculate the velocity from an acceleration time

graph

- The area between the acceleration time graph and

the x-axis is the velocity of the object.

Sample Problem

- What is the velocity of the object after 10

seconds?

Sample Problem (contd)

- To calculate the velocity, you would find the

area of the shaded region.

Sample Problem (contd)

Constant Positive Velocity

Constant Negative Velocity

Positive Velocity with Positive Acceleration

Positive Velocity with Negative Acceleration

Negative Velocity with Positive Acceleration

Negative Velocity with Negative Acceleration

Hyperlink to TI interactive Graphs

Acceleration Equations

- a acceleration in m/s2
- ?v - change in velocity in m/s
- vf final velocity in m/s
- vi initial velocity in m/s
- ?t or t time interval in seconds
- d displacement in m

Acceleration equations

- Since velocity, displacement, and acceleration

are all vector quantities, you must keep

direction in mind when you substitute values into

the equations. Up or to the right are considered

to be positive directions. Down or to the left

are considered to be negative directions.

Sample Problem

- It takes 4.8 seconds for a cars speed to

increase by 10 m/s. What is its acceleration?

Given ?v 10m/s t 4.8 sec a ?

Answer a 2.08 m/s2

Sample Problem

- A rocket is capable of accelerating at 800 m/s2.

How long after lift off will the rocket reach 500

m/s?

Given a 800 m/s2 vf 500 m/s vi 0 m/s t ?

Answer t 0.625 sec

Sample Problem

- A car is traveling at 50 m/s must slow down to 30

m/s in the next 10 m. What deceleration must the

car have?

Given vi 50 m/s vf 30 m/s d 10 m a ?

Sample Problem

- A car moves at 12 m/s and coasts up a hill with a

uniform acceleration of -1.6 m/s2. How far has

it traveled after 6 sec? How far has it gone

after 9 sec?

Answer 43 m 43 m

Sample Problem

- An engineer must design a runway to accommodate

airplanes that must reach a ground velocity of 61

m/s before they take off. These planes are

capable of being accelerated uniformly at the

rate of 2.5 m/s2. How long will it take the

planes to reach takeoff speed? What must be the

minimum length of the runway?

Answer 24 sec 740 m

Sample Problem

- As a traffic light turns green, a waiting car

starts with a constant acceleration of 6 m/s2.

At the instant the car begins to accelerate, a

truck with a constant velocity of 21 m/s passes

in the next lane. How far will the car travel

before it overtakes the truck? How fast will the

car be traveling when it overtakes the truck?

HINT Set the two distances equations equal to

each other.

Acceleration due to gravity

- If an object is dropped or thrown, it will fall

under the acceleration of gravity and its

acceleration is 9.8 m/s2, down. The entire time

the object is in the air, it has an acceleration

of 9.8 m/s2, down, but its velocity is constantly

changing. On the way upward, the speed is

decreasing and on the way down, the speed is

increasing.

Acceleration due to Gravity

- Keep in mind that acceleration is a vector

quantity so when it is used in an equation, you

use a or - sign to indicate whether the

direction is up or down. Since the acceleration

due to gravity is 9.8 m/s2, down when it is

substituted into the equations you will use -9.8

m/s2.

Gravity equations

- You will use the same equations however, you will

use the value of -9.8 m/s2 for the acceleration

when an object is in freefall.

Sample Problem

- A stone falls freely from rest for 8 seconds.

What is the stones velocity after 8 seconds?

What is the stones displacement during this time?

Answer -78 m/s -310 m

Sample Problem

- Kyle is flying a helicopter that is rising at 5

m/s when he releases a bag. After 2 seconds,

what is the bags velocity? How far has the bag

fallen? How far below the helicopter is the bag?

Answer -15 m/s -10 m 20 m

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