Chapter 2 Motion Electric Bullet Trains in Japan can achieve speeds up to 270km/hr. They are very quiet and have a great safety record.

Chapter 2 Table of Contents Sec. 2-1 Motion is Relative Sec. 2-2 Speed Sec. 2-3 Velocity Sec. 2-4 Acceleration Sec. 2-5 Free Fall: How Fast Sec. 2-6 Free Fall: How Far Sec. 2-8 How Fast, How Far, How Quickly How Fast Changes Calculator Programming

Sec. 2-1 Motion is Relative Ex: You are at rest relative to your desk, but you are moving at 30km/sec. Relative to the sun!

Kim’s Frame of Reference

Joe’s Frame of Reference

Displacement As an object moves from one place to another, drawn from the initial position to the final position is the displacement.

Displacement displacement is The football player ran a great distance, but his displacement is nearly.

Displacement Although the distance you travel from Eugene to Salem may vary, your displacement will always be the straight line distance between the two cities.

Displacement displacement = change in position = The gecko moving along the x-axis from x i to x f undergoes a displacement of

Displacement Check A space shuttle takes off from Florida and circles the Earth several times, finally landing in California. While the shuttle is in flight, a photographer flies from Florida to California to take pictures. Who undergoes the most displacement?

Sec. 2-2 Speed or, the at which distance is covered or, distance covered unit of time The speed at any instant of time is called instantaneous speed.

Mathematics of Speed average speed is a good way to measure object which vary their speed Example units: mi/hr, cm/day, km/hr, or m/s

Check Question If you ride a bike a distance of 5m in 1 sec, what is your speed? For 10m in 2 sec? For 100m in 20 sec?

Sec. 2-3 Velocity Velocity is the speed of an object in a given direction. Ex: 60 km/hr north, 5m/s down more on vectors in chapter 6

Constant velocity Requires change in direction is a change in velocity even though the speed has not changed constant direction

Graphical Analysis

Displacement vs. Time Graph The slope of this graph = rise / run =  d /  t =  x /  t

Changing Velocity If either the speed or direction or both is changing then you have a change in velocity.

Changing Velocity In this loop on the Corkscrew the speed is constant but the velocity is changing due to the continuous changes in direction.

Changing Velocity The green vectors (arrows) below represent velocity. Name the two the velocity is changing in the picture below.

Sec 2-4 Acceleration Acceleration = acceleration is the rate at which velocity is changing. key word - -applies to both increases and decreases in speed increase: positive acceleration Decrease: (assume no change in direction in this chapter)

Acceleration a decrease in speed is a negative acceleration could also be called a deceleration.

Acceleration Acceleration is any change in velocity. It is the acceleration that you feel, not the velocity.

Acceleration Check #1 You are traveling in a car down the highway at a constant velocity. No bumps or curves in the road to change direction and produce an acceleration. Now cover up the windows!

Acceleration Check #2 Cont’d Do you know how fast you are moving? Do you even know that you are moving? You do not feel constant velocities! You do feel accelerations! What do you pay for at the amusement park?

Acceleration Check #2 How much acceleration does a car have if it goes from 0km/hr to 100km/hr in 10 sec.?

Acceleration Check #2 How much acceleration does a car have if it goes from 0km/hr to 100km/hr in 10 sec.?

Acceleration Check #2 How much acceleration does a car have if it goes from 0km/hr to 100km/hr in 10 sec.?

Acceleration Check #2 How much acceleration does a car have if it goes from 0km/hr to 100km/hr in 10 sec.?

Acceleration Check #3 What is the acceleration of an object that moves from 2-10 m/s in a time of 2 sec?

Acceleration Check #3 What is the acceleration of an object that moves from 2-10 m/s in a time of 2 sec?

Acceleration Check #3 What is the acceleration of an object that moves from 2-10 m/s in a time of 2 sec?

Acceleration Check #3 What is the acceleration of an object that moves from 2-10 m/s in a time of 2 sec?

Billiard Ball The motion in this picture took place in 1.00 sec. You would only see a blur. Is this ball accelerating? Yes. How can you tell? Is the acceleration constant? What would happen if it attained a negative acceleration?

Position vs. Time graphs has been concerned with the multiple means by which the motion of objects can be represented. Include the use of words, the use of diagrams, the use of numbers, the use of equations, and the use of graphs. to describe motion. The specific features of the motion of objects are demonstrated by the shape and the slope of the lines on a position vs. time graph. consider a car moving with a constant, rightward (+) velocity - say of +10 m/s.

Position vs. Time graphs The graph would look like the graph at the right. a motion described as a constant, positive velocity results in a line of constant and positive slope when plotted as a position- time graph.

Position vs. Time graphs Now consider a car moving with a rightward (+), changing velocity - that is, a car that is moving rightward but speeding up or accelerating. a motion described as a changing, positive velocity results in a line of changing and positive slope when plotted as a position-time graph

Position vs. Time graphs Match the appropriate car with the appropriate letter

Position vs. Time graphs Match the appropriate car with the appropriate letter Red constant velocity,B Blue,A; Green,C

Position vs. Time graphs

Velocity vs. Time graphs

Position vs. Time graphs

Sec. 2-5 Free Fall: How fast All objects that fall have two forces acting on it. Gravity Air resistance

Free Fall: How fast Free fall object (no air resistance) by definition. Acceleration due to gravity is approximately 10m/s 2, what does this mean?

Instantaneous Velocities of Free Fall Objects

Instantaneous Velocity Calculation The symbol for acceleration due to gravity is “g” =9.8 m/s 2 for more accuracy. From the previous table (fig 2-2 in text) we can form the mathematical relationship for “v.”

Instantaneous Velocity Check If an object is dropped from a rest position at the top of a cliff, how fast will the object be moving after falling for 1 sec.?

Instantaneous Velocity Check If an object is dropped from a rest position at the top of a cliff, how fast will the object be moving after falling for 1 sec.?

Instantaneous Velocity Check If an object is dropped from a rest position at the top of a cliff, how fast will the object be moving after falling for 1 sec.?

Hammer and Feather What would hit the ground first when dropped? A hammer or a feather? The hammer of course but why? What if we would ignore air resistance? Would the hammer still hit first? Remember v=gt, the object with greater “v” will hit first.

They both have the same “g” acting on them. Therefore in v=gt both the velocity and the time would be the same, and they would hit at the same time. There is very little air resistance on the moon so here is the experiment as performed during the Apollo 15 journey to the moon.

Another Drop Experiment

Feather and Ball in Vacuum When there is no air resistance,

At the right the acceleration of the ball as it moves upward is -10m/s 2 As it moves downward its acceleration is 10m/s 2

What is it’s acceleration just past the peak? 10m/s 2 What is it’s acceleration at the peak?(Hint: Acceleration is how much the velocity is changing. Has the velocity stopped changing at the peak?) 10 m/s 2

Average Velocity How do we find the average velocity for an object moving in a straight line? The same way we find the average of 2 numbers in math, add them up and divide by 2. To find average velocity we will add v i and v f and divide by 2.

Average Velocity Calculation Lets go back to the falling object. After 1 sec. It has a velocity of 10 m/s. What is the average velocity during this first second.

Average Velocity Calculation Lets go back to the falling object. After 1 sec. It has a velocity of 10 m/s. What is the average velocity during this first second.

Average Velocity Calculation Lets go back to the falling object. After 1 sec. It has a velocity of 10 m/s. What is the average velocity during this first second.

Average Velocity Calculation This means that an in the first second has an average velocity of 5m/s. It will travel 5 m in the first second.

Eric Nelson (2001)

Sec. 2-6 Free Fall: How far How fast is entirely independent from how far it will move.

After 1 sec the object has an instantaneous speed of 10 m/s Does this mean it falls a distance 10 m during the first second? No It was moving near 0 m/s when first dropped and eventually reached 10 m/s after 1sec. The average speed was 5 m/s so it fell 5 m in the first second.

Here is a table of the distances objects travel in free fall in one second intervals. Notice the relationship that results.

How long does it take a car to travel 30.0 m if it accelerates at a rate of 2.00 m/s 2 ?

5.48 sec.

Practice A car starting from rest is accelerated at a constant rate of 6.2 m/s 2. How far does the car travel during the first 7 sec. of acceleration? D=.5gt 2 D=.5gt 2 =.5 X 6.2 m/s 2 X 7sec 2 D=.5gt 2 =.5 X 6.2 m/s 2 X 7sec 2 =152m

Activity: Time Interval of Free Fall Acquire: 1 meterstick, 1 friend Determine your reaction time by having a friend hold a meterstick vertically between the thumb and index finger of your open hand. The meterstick should be held so that the zero mark is between your fingers with the 1 cm mark above it.

Activity: Time Interval of Free Fall cont’d Have your friend drop the meterstick without warning. Catch it as quickly as you can, record the distance measurement.. 15 trials each You know acceleration due to gravity and distance, calculate your reaction average time.

Sec. 2-8 How Fast, How Far, How Quickly How Fast Changes Much confusion comes from mixing up “How fast” with “How far.” Speed and velocity use How far, distance