Motion & SpeedStart KinematicsStart Kinematics

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Motion & Speed

Remember the lightning?

When lightening strikes, you see a When lightening strikes, you see a flash of light.flash of light.

Some seconds later, you hear the Some seconds later, you hear the thunder.thunder.

The thunder is SOUND arising The thunder is SOUND arising from the sudden expansion of the from the sudden expansion of the air at the time of the flash.air at the time of the flash.

How do we explain the delay?How do we explain the delay?

Science Measures So what can we measure?

We know how to measure distance (meter stick).We know how to measure time (clock).We know that the lightening strikes at a particular

point, but we can’t PREDICT where it will hit.We can’t do much with this experiment.Let’s think about a new one.

DefinitionIf something takes a time (t) to travel

a distance (x), we can define the speed (s) as

t

xsspeed

time

distance

For the moment, the object is assumed to be traveling in a straight line

(From the textbook)

Average Speed (defined)

Average speed is defined as the total distance traveled divided by the time it took to cover this distance.

(A bar is often used over a symbol to indicate its average value.)

speed) (average taken)(time traveleddistance

d=s x t

t

ds

So..The distance traveled during this interval of

time is simply the speed multiplied by the time.

Example:You are traveling at 80 miles an hour. How far

would you travel in 30 minutes?Distance=speed x time.

40miles hour 2

1 80

hour

milesd

And about $2.00 in gasolineAnd a traffic ticket!

A historical experiment

CannonGuy with stop watchLight … start watchBoom … stop watch

stopwatch on the time

man cannon to from distance sound of speed

D

In 1635The philosopher Pierre Gassendi did this

experiment. He got 478 m/s and did not own a Rolex. (50% high)

A few years later Mersenne did the experiment and got 450 m/s

In 1738 a team from the Paris Academie des Sciences got 344 m/s

Accepted value: 343 m/s or 1125 ft/secThe big mistake that Gassendi and

Mersenne made seems to be having ignored the effect of the wind.

Speed of sound

We will take it as

1100 ft/secThis is about 1/5th of a mile

Knowing that the speed of sound is about 1/5th of a mile/second …

When you see lightening, start counting off the seconds … one and two and three and … etc.

When you hear the thunder, stop counting.Divide the number you stopped at by 5. (d=s

x t)s=1/5 mils/sec.

That is how far the lightening strike was from where you are standing. (in miles.)

Ponder

If you hear the thunder at the same time that you see the

lightening, how dead are you?

Measuring Speed

To measure speed, we used a device for measuring distance,such as a ruler,

and one for measuring time, such as a clock.

These mile markers and your wristwatchgive you all the information you need to

determine average speeds.

Images of SpeedA blurred painting or photograph such as

that in the figure is one way to “see” motion.

Images of Speed

A multiple-exposure photograph is a method that also provides a way of measuring the speed of an object.These photographs are made in a totally dark

room with a strobe and a camera with an open shutter. A strobe is a light source that flashes at a constant, controllable rate—about 10 millionths of a second—producing a still image of the moving object.

What’s Happening Here?

Images of Speed If the strobe flashes 10 times per

second, the resulting photograph will show the position of the object at time intervals of 0.1 second. Thus, we can “freeze” the motion of the object into a sequence of individual events and use this representation to measure its average speed within each time interval.

Images of SpeedAs an example of measuring average

speed, let’s determine the average speed of the puck in the figure below.

Images of Speed

The puck travels from a position near the 4-cm mark to one near the 76-cm mark: a total distance of 72 centimeters.

Because there are seven images, there are six intervals. The total time taken is six times the time between flashes—

that is, 0.6 second.

Therefore, the average speed is:

Working It Out: Average Speed

If you know the average speed, you can determine other information about the motion. You plan to drive 60 miles with the cruise

control set at 50 mph. How long will it take to get there?

You plan to maintain an average speed of 50 mph on an upcoming trip. How far can you travel if you drive an 8-h day?

Average Speed vs. Instantaneous Speed

Suppose you live 40 miles from school and it takes you 2 hours to drive home. Your average speed during the trip is:

This means that, on the average, you travel a distance of 20 miles during each hour of travel.

Still: You may have stopped at traffic lights (0 mph); You may have traveled at 50 mph at some point.

The use of average speed disregards the details of the trip.

Average Speed vs. Instantaneous Speed

Actually, the definitions of average and instantaneous speeds are quite similar. They differ only in the size of the time interval involved.

If you want to know how fast you are going at a given instant, try studying the motion during a very small time interval. The instantaneous speed is equal to the average speed over a time interval that is very, very small.

Instantaneous speed, rather than the average speed, plays

an important role in the analysis of nearly all realistic motions.

Note:

Definition of Instantaneous Speed

This more complete description of motion tells us how fast you were traveling at any instant during your trip.

A speedometer tells you thecar’s instantaneous speed.

Some DefinitionsIf you travel a total distance D in time “t”,

the average speed is:<speed>=<s>= s =D/t

We use the Greek letter “” to indicate very SMALL changes.

If you travel a tiny distance x in miniscule time “t”, the instantaneous speed s is:instantaneous speed:

t

xs

Measure This!

The fastest things you might ever try to measure:Light: 186,000 mps (miles / sec)Planet Earth: 67,000 mphThe sound of music: 1100 ft/sec

The slowest things you might try to measure:The giant sloth: 0.07 mphContinents: 1 cm / year

Let’s take a trip …

Travel from A to B at 50 miles per hour.How long does it take to make this trip if A

and B are 50 miles apart?

Do you want to reconsider?

A BA

We need to specify the PATH!

Volunteer

Come to the front of the roomTake three stepsStop

You are wrong!

Vectors

Speed with Direction

Objects do more than speed up and slow down. They can also change direction, while maintaining their speed, or changing both speed and direction at once.

Either the average speed or the instantaneous speed tells us how fast an object is moving, but neither tells us the direction of motion.

VectorThe magnitude of a quantity is represented

by the LENGTH of an arrow (vector)The direction is specified by the direction of

the arrow.

Example10 steps to the right:

10 Steps up

10 steps to the right and 10 Steps up

SumA+B

A

B

More Definitions

Speed is a scalar quantity. No direction.Velocity is a speed and a direction of that

speed together. It is a vector

Ponder: A woman jogs from A to B to C to D in 30 minutes

What was the average speed of the woman?What was the average velocity of the woman?Is she fast? Which of these two quantities

addresses this question?

Rectangle

A D

CB

0.5 m

1.0 miles

Let’s move on …