Chapter 2 Linear Motion

Relative Motion  Relative Motion: Regarded in relation to something else. It depends on a point of view or frame of reference.  Train Example: There are two people, one in the train and the other watching from the road. If the person in the train throws the ball, what does the path of the ball look like Relative to the passenger in the train Relative to the person on the side of the road

Our Relative Motion  North or ‘Up’ will be negative.  South or ‘Down’ will be positive.  East or Right will be positive.  West or Left will be negative.

Definitions…  Rate: A quantity divided by time.  Speed: The measure of how fast something is moving. Speed is the distance covered per unit of time.  Instantaneous Speed: The speed at any given instant.

Average Speed When you are talking about the speed over a period of time, you are actually calculating the average speed. The average speed is defined as…

Average vs Instantaneous Speed

Velocity  Velocity: direction. The speed in any given direction.  Constant Velocity: BOTH If an object has constant velocity, it has to have BOTH a constant speed and a constant direction  Changing Velocity: EITHER If EITHER the speed or direction is changing, then the velocity is changing.

Abbreviation and Unit for Speed and Velocity  We will abbreviate BOTH speed and velocity with a lower case v.  The unit for speed and velocity is meters per second (m/s)

Acceleration  Acceleration: The rate at which the velocity is changing.  The equation for average acceleration is… ∆ means “change in”

Abbreviation and Units for Acceleration  We abbreviate acceleration with a lowercase a.  The unit for acceleration is m/s 2.

Find the car that is accelerating…

Vectors  Vectors show magnitude (size) and direction.  We represent vectors with arrows.

Velocity and Acceleration

Free Fall  Free Fall: An object is in free fall when there is little or no air resistance and gravity is the only force affecting a falling object.  Elapsed time: The time that has passed since the beginning of the fall.

Gravity  The force that pulls objects towards the earth. This is also known as the acceleration due to gravity.  Gravity is 10 m/s 2.  Gravity is abbreviated with the letter,g.

Another Equation… Since gravity is acceleration, we can take the equation from before -  a=v/t  And substitute g for a  g=v/t You can use gravity to find the distance that an object drops using the following equation…  d=(1/2)gt 2

Think about Acceleration  Joe throws a ball into the air. What is the velocity at the top of the parabola? What is the acceleration at the top?  Think about the pirate ride at an amusement park. 40 m/s

Get Out Your Velocity, Acceleration, and Gravity Worksheet in your Packet

Problem Solving Strategies… 1.Write the word given 2.Write down all that is given in your problem 3.Write a ? Mark 4.Write what the question is asking for 5.Write down solution or soln 6.Write the equation that you will be using and plug in the information from the givens.

#1 Benjamin watches a thunderstorm from his apartment window. He sees a flash of lightening and begins counting until he hears the clap of thunder 10.0 seconds later. Assume that the speed of sound is m/s. How far away was the lightening bolt? Given: t=10 sec v=340 m/s ?=d Soln or Solution: d=vt d=340 m/s*10 sec d=3,400 m

#2. Grace is driving her sports car at 30 m/s when a ball rolls out into the street in front of her. Grace slams on the brakes and comes to a stop in 3.0 sec. What was the acceleration of Grace’s car? Given: v=30 m/s t=3.0 sec ?=a Soln or Solution: a=v/t a=30 m/s / 3.0 sec a=10 m/s 2

Find a Partner and Continue to Work on the Rest of Your Worksheet!

Graphs of Motion

Problem… Why is a car’s gauge called a speedometer and not a velocitiometer? Speed is how fast something is moving Velocity is the speed in a given direction.

Slope of Graphs of Motion  When looking at a graph, you can find the slope of a line by using the following equation… (x 1,y 1 )=(5,50) (x 2,y 2 )=(1,10)

Distance vs Time Graphs  A motion with a constant positive velocity results in a line of constant and positive slope when plotted as a position-time graph. Consider a car moving with a constant, rightward (+) velocity of 10 m/s. Dependant Variable Independent Variable

Distance vs Time Graphs  A motion with changing positive velocity results in a line of changing and positive slope when plotted as a position-time graph Consider a car moving with a changing rightward (+) velocity. That is, the car is moving rightward and accelerating.

The Slope of a Distance-Time Graph  What is the equation to find slope?  What is the equation to find velocity?  What is the variable on the y-axis on a distance-time graph?  What is the variable on the x-axis on a distance-time graph?

As the slope goes, so goes the velocity Slow, Rightward Constant Velocity Fast, Rightward Constant Velocity Slow, Leftward Constant Velocity Fast, Leftward Constant Velocity

Which Car Has The Greater Velocity?

Velocity-Time Graph  A motion with constant, positive velocity results in a line of zero slope when plotted on a velocity-time graph. Consider a car moving with a constant, rightward (+) velocity of 10 m/s. Remember a car moving with a constant velocity has a zero acceleration.

Velocity-Time Graph  A motion with changing, positive velocity results in a diagonal line when plotted as a velocity-time graph. The slope of this line is positive, corresponding to the positive acceleration. Consider a car moving with a rightward (+), changing velocity - that is a car that is moving rightward and speeding up or accelerating.

Constant Velocity & Changing Velocity  The velocity vs time graphs for the two types of motion - constant velocity and changing velocity (acceleration).

Positive/Negative Velocity

Slope of a Velocity-Time Graph  What is the equation for slope?  What is the equation for acceleration?

Slope (V-T Graph)= Acceleration

Which car…

Check Your Understanding  Consider the graph at the left. True/False is the object… a.Moving in the positive direction b.Moving with a constant velocity. c.Moving with a negative velocity. d.Slowing down. e.Changing directions. f.Speeding up. g.Moving with a positive acceleration. h.Moving with a constant acceleration. True- in the + region False- not a straight line False- line in + region True- approaching x-axis False- never crosses axis False- not moving away from axis False- see above True- line is diagonal