Current Event• Choose an article that is at least 2 pages in length if it is

in a magazine or at least 1 column if it is in a newspaper. If it is on the internet it should be a 5-8 paragraphs.

• Read the article and write a summary of what the main points of the article included.

• On Friday we will discuss the articles. You should be working from your summary during the discussion, though you can bring the article in if you want to.

• You will turn the summary in at the end of the period. No late summaries will be accepted.

• This article should concern either physics, weather, astronomy or geology. NO BIOLOGY OR MEDICINE!

Linear Motion - Kinematics

Key Terms

• Speed• Velocity• Acceleration• Free fall• Gravity• Distance• Displacement

Linear Motion• Motion in a straight line• This motion can be described several ways:

– Speed– Velocity– Acceleration– Distance– Direction

• How can you tell when an object is moving?– All motion is relative– Things that appear to be at rest can move

Motion is Relative• Must compare two objects relative to one

another. Called a frame of reference• How can you tell when an object is moving?

– All motion is relative– Things that appear to be at rest can move

• Example:– You are sitting in class in your chair – are you

moving?– Although you may be at rest relative to Earth’s

surface, you’re moving about 100,000 km/h relative to the sun.

SpeedSpeed is one way to describe motion. It describes how fast an object is

moving using distance and time. Average speed is the total distance traveled over the total time and instantaneous speed is the speed at a particular moment

For example, 30 miles per hour means object travels distance of 30 miles in an elapsed time of one hour. Write as,

(SPEED) =(Distance traveled)

(Time elapsed)

30 miles per hour = 30 miles

hour

Practice:

What is the average speed of a cheetah that sprints 100 meters in 4 seconds? How about if it sprints 50 meters in 2 seconds?

A car has an average speed of 100 kilometers per hour. How far does it travel in 30 minutes?

Demo: Ball Races

Which ball wins the race, A or B?A

BFinishLine

Which ball has the larger average speed?Which has the larger instantaneous speed at each point.

Velocity

• a description of how fast and in what direction• a vector quantity• Constant velocity is constant speed and

constant direction (straight-line path with no acceleration).

• Constant speed is steady speed, neither speeding up nor slowing down.

Different types of velocity and speed

• Average velocity/speed• A value summarizing the

average of the entire trip.• All that’s needed is total

displacement/distance and total time.

• Instantaneous velocity• A value that summarizes

the velocity or speed of something at a given instant in time.

• What the speedometer in you car reads.

• Can change from moment to moment.

When we say that an object is moving at constant velocity we mean that it is 1) at rest, 2) moving at an unchanging speed, 3) moving at an unchanging speed in a straight-line path, and that its acceleration is 4) zero. 5) constantly increasing (or decreasing). 6) uniform.

Practice

The speedometer of a car moving east reads 100 km/h. It passes another car moving west at 100 km/h. Do they have same speed? Velocity?

During a certain period of time, the speedometer of a car reads a constant 60 km/h. Does this indicate a constant speed? Constant velocity?

Practice Problem

A car going 15m/s accelerates at 5m/s2 for 3.8s. How fast is it going at the end of the acceleration?

First step is identifying the variables in the equation and listing them.

Practice Problem

A car going 15m/s accelerates at 5m/s2 for 3.8s. How fast is it going at the end of the acceleration?

t=3.8s

vi=15m/s

a=5m/s2

vf=?

Hidden Variables

• Objects falling through space can be assumed to accelerate at a rate of –9.8m/s2.

• Starting from rest corresponds to a vi=0

• A change in direction indicates that at some point v=0.

• Dropped objects have no initial velocity.

Practice Problem 2

• A penguin slides down a glacier starting from rest, and accelerates at a rate of 7.6m/s2. If it reaches the bottom of the hill going 15m/s, how long does it take to get to the bottom?

AccelerationDefine acceleration as how fast velocity changesAcceleration is a rate of a rate (units will have 2 time

values)

(ACCELERATION) = (Change in Velocity)

(Time interval)

Note: An object accelerates anytime its velocity changes. Examples include:

Object speeds up.Object slows down Object changes direction (curved path)

Best example of acceleration is objects in free fall

Acceleration

Free-fall• falling under the influence of gravity only

—with no air resistance– freely falling objects on Earth gain

speed at the rate of 10 m/s each second (more precisely, 9.8 m/s2)

Gravity• Gravity causes an acceleration.• All objects have the same acceleration due to

gravity.• Differences in falling speed/acceleration are

due to air resistance, not differences in gravity.• g=-9.8m/s2

• When analyzing a falling object, consider final velocity before the object hits the grounds.

Acceleration

Galileo first formulated the concept of acceleration in his experiments with inclined planes.

• When we say that an object is being accelerated, we mean that

• 1) it is at rest, • 2) it is moving, • 3) it is either at a state of rest or a state of constant

velocity, • 4) its state of motion is changing,and we define acceleration to be • 5) a change in speed. • 6) a change in velocity. • 7) the rate at which speed changes. • 8) the rate at which velocity changes.

• An object is accelerating if it moves • 1) with constant velocity • 2) in a circular path • 3) in a straight-line path

because it is undergoing a change in its • 4) speed. • 5) direction• 6) net force.

• A car increases its speed from 60 to 65 miles per hour in the same time that a bicycle increases its speed from rest to 5 miles per hour. In this case the acceleration is greater for the

• 1) car, • 2) bicycle, • 3) is the same for each,

principally because • 4) the car undergoes the greater change in velocity. • 5) the bicycle has considerably less mass. • 6) both undergo equal increases in speed during the

same interval of time.

Equation for displacement

t

dv

fi vvv 21

tvd

tvvd fi 21

Practice Problems

• A car slows from 45 m/s to 30m/s over 6.2s. How far does it travel in that time?

A cyclist speeds up from his 8.45m/s pace. As he accelerates, he goes 325m in 30s. What is his final velocity?

Equation that doesn’t require vf

tvvd fi 21 atvv if

tatvvd ii 21

)2(21 atvtd i

2

21 attvd i

Practice ProblemsA ball rolling up a hill accelerates at –5.6m/s2

for 6.3s. If it is rolling at 50m/s initially, how farhas it rolled?

If a car decelerates at a rate of –4.64m/s2

and it travels 162m in 3s, how fast was it going initially?

An equation not needing t tvvd fi 2

1atvv if

atvv if

ta

vv if

a

vvvvd iffi2

1

a

vvd if

22

21

222 if vvad

A bowling ball is thrown at a speed of6.8m/s. By the time it hits the pins 63m away, it is going 5.2m/s. What is theacceleration?

The Big 4

atvv if advv if 222

tvatd i 2

21 tvvd fi 2

1

A plane slows on a runway from 207km/hrto 35km/hr in about 527m.

a. What is its acceleration?b. How long does it take?

Ticker Tapes• A common way of analyzing the motion of objects in physics labs is to perform a

ticker tape analysis. A long tape is attached to a moving object and threaded through a device that places a tick upon the tape at regular intervals of time – say every 0.1 second. As the object moves, it drags the tape through the "ticker," thus leaving a trail of dots. The trail of dots provides a history of the object's motion and is therefore a representation of the object's motion.

• The distance between dots on a ticker tape represents the object's position change during that time interval. A large distance between dots indicates that the object was moving fast during that time interval. A small distance between dots means the object was moving slow during that time interval. Ticker tapes for a fast-moving and a slow-moving object are depicted below.

• The analysis of a ticker tape diagram will also reveal if the object is moving with a constant velocity or with a changing velocity (accelerating). A changing distance between dots indicates a changing velocity and thus an acceleration. A constant distance between dots represents a constant velocity and therefore no acceleration. Ticker tapes for objects moving with a constant velocity and an accelerated motion are shown below.

Uniform Motion

Position vs. Time Graph                      Velocity vs. Time Graph

Nonuniform Motion - Changing Velocity

Position vs. Time Graph                     Velocity vs. Time Graph

•Q: What does the slope on a Position vs. Time Graph tell us?

•Q: What does the slope on a Velocity vs. Time Graph tell us?

•A: The slope on a Position vs. Time Graph tells us the velocity. A positive slope indicates a positive velocity. A negative slope indicates a negative velocity.

•A: The slope of a velocity vs. time graph tells us the acceleration. A positive slope indicates a positive acceleration. A negative slope indicates a negative acceleration.

The slope or gradient of a distance-time graph is increases with speed.

dis

tan

ce

time

slow

fast

Question 2Describe the motion of the three buses X, Y and Z shown in the graph below.

Uniformly Accelerating Objects

• You see the car move faster and faster. This is a form of acceleration.

• The position vs time graph for the accelerating car reflects the bigger and bigger x values.

• The velocity vs time graph reflects the increasing velocity.

Velocity-time graphs

velo

city

time

low acceleration

high

acc

eler

atio

nThe slope of a velocity-time graph represents acceleration.

deceleration

constant velocity or zero acceleration

Constant Velocity

• This graph shows that the velocity:

1. is 1 m/s. 2. stays constant at 1 m/s

for 10 seconds.

Activity #1 – Predicting the fall time of a ball

• Predict how long it will take for a ball to fall _____ meters

• Show all your work and calculations• Test your hypothesis and actually time the fall• Perform at least 8 trials and find the average

fall time• Plug your time and distance values into an

equation to find the acceleration (a or g) and see how close your value comes to 9.8 m/s/s

Activity #2 – Reaction Time

Use a ruler/meter stick and calculate your reaction timeCompare this to class/larger sampling size averagesHave one partner hold a ruler/meter stick vertically. The other

partner places their hand at the 0 cm mark. Catch the ruler and record the distance.

Record the drop distance in cm 5 times and find the averageCalculate your average reaction time using the distance formula,

being careful to make sure your units are converted!The average reaction time for the general population is

approximately 0.2 – 0.25 seconds

Activity #3 – Tin pan alley• Galileo conducted an experiment similar to this to help him

determine the equation for free fall in relation to distance, time and gravity.

• Attach a set of 6 ½ inch hex nuts to a string so that the nuts will hit the pie pan at equal time intervals

• Place your first hex nut at 15 cm• The falling nuts will accelerate (speed up) as they fall due to

gravity. How will you have to place your hex nuts on the string so that the “clangs” occur at equal time intervals?

• Are there any equations that can help you calculate the proper distances?

• Record the exact spacing between the nuts that resulted in the clangs occurring at equal time intervals. Show all calculations!!