CHAPTER 11: MOTION

Section 1: Measuring Motion

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Observing Motion•How do you determine if something is moving?•Is a person sitting in a driving car moving?

•What about a character in a video game that is apparently running across the TV?

•If the earth is orbiting the sun, are you moving now?

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Observing Motion•The motion of an object must be observed in relation to objects that stay in place, or reference points

•Frame of Reference: used to describe the motion of an object relative to reference points•When an object changes position with respect to a frame of reference, the object is in motion

• Mythbusters

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Observing Motion•Consider the person sitting in the car…

•Describe their motion from each frame of reference:•Inside the car

•Moving very fast•A car driving past

•The person is slowly moving backwards

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Observing Motion•Distance: measures the path taken

•Displacement: the change of an object’s position•always includes direction

Bill Nye Frame Of Reference and Law of Inertia

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Speed and Velocity

•Speed: the distance traveled divided by the time interval in which the motion occurred

•Velocity: the speed of an object in a particular direction

•Speed tells us how fast an object moves, and velocity tells us how fast the object moved (speed) AND the direction the object moved

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Velocity

•Velocity is described relative to a reference point•North, west, east, south, etc.

•It can also be described as motion from a fixed line

•Direction is described as positive or negative along the line of motion•Up and right are usually positive velocity•Down and left are usually negative velocity

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Velocity•Could something have a negative velocity?

•Yes, that means it is going backwards

•Is it possible for something to have a negative speed?•No, there is no specific direction

•Is it possible for something to have a constant speed but a changing velocity?•Yes, all the object has to do is turn•Remember, velocity includes direction, speed does not

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Calculating Speed•Average speed is calculated as distance divided by time

•Constant Speed: equal distances in equal amounts of time

•Instantaneous Speed: the speed at any given time

distancespeed = ,

tim or

e

dv

t

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Units

•The SI unit for speed is meters per second (m/s)•Remember! We use the metric system in science

•Instead of using miles per hour (mph), we use meters per second (m/s) or kilometers per hour (km/h)

•The smaller the unit, the more precise the measurement

•You will need to make conversions in your math problems!

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Math skills: VelocityMetal stakes are sometimes placed in glaciers to help measure a glacier’s movement. For several days in 1936, Alaska’s Black Rapids glacier surged as swiftly as 89 meters per day down the valley. Find the glacier’s velocity in m/s. Remember to include direction.

1. List the given and the unknown values.Given: time - t = 1 day

distance - d = 89 m down the valley

Unknown: velocity - v = ? (m/s and direction)

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Math skills: Velocity

2a. Perform any necessary conversions.To find the velocity in meters per second, the value for time must be in seconds.

t = 1 day = 24 h x 60 min x 60 s 1 hr 1 min

t = 1 day = 24 x 60 x 60

t = 86,400 s = 8.64 x 104 s

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Math skills: velocity

2b. Write the equation for speed

3. Insert the known values and solve.

distancespeed = , or

time

dv

t

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89 m (For velocity, include direction.)

8.64 10 s

dv

t

31.0 10 m/s down the valleyv

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SECTION 2: ACCELERATION

Chapter 11: Motion

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Acceleration

•Acceleration: the rate at which velocity changes over time

•Acceleration can be a change in speed•An increase or decrease in speed is an acceleration

•Acceleration can be a change in direction•A motorcyclist who rides around the inside of a barrel is constantly accelerating

•Acceleration can be BOTH a change in speed AND direction

NFL Science of Football: kinematics

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Acceleration•For straight line motion, a positive acceleration means the object’s velocity is increasing •The object is speeding up

•A negative acceleration means that the object’s velocity is decreasing •The object is slowing down

•Centripetal Acceleration: acceleration that occurs in circular motion

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Acceleration

•A constant (unchanging) velocity means no acceleration

•A constant acceleration means a constantly changing velocity

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Acceleration

•To calculate acceleration subtract the initial velocity (vi) from the final velocity (vf) and divide by time

a = vf – vi or a = v

t t•The SI unit for acceleration is m/s2 (m/s/s)

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Math skills: accelerationA flowerpot falls off a second-story windowsill. The flowerpot starts from rest and hits the sidewalk 1.5 s later with a velocity of 14.7 m/s. Find the average acceleration of the flowerpot.

1. List the given and the unknown values.Given: time - t = 1.5 s

initial velocity - vi = 0 m/sfinal velocity - vf = 14.7 m/s down

Unknown: acceleration - a = ? (m/s2 and direction)

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Math skills: Acceleration

2. Write the equation for acceleration.

3. Insert the known values into the equation, and solve.

acceleration = final velocity – initial velocity

time = vf – vi

t

14.7 m/s 0 m/s

1.5 s f iv v

at

214.7 m/s9.8 m/s down

1.5 s a

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Graphing motion•Speed is shown with a distance vs. time graph of its motion•x-axis: time (ind. variable)•y-axis: distance (dep. variable)

•The slope of the line represents the speed•The speed can be found by calculating the slope

•A straight line means a constant speed

How to read and interpret graphs

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Graphing Motion

•Acceleration is shown with a speed vs. time graph•x-axis: time (ind. variable)•y-axis: speed (dep. variable)

•The slope of the line represents the acceleration•A positive slope means an object is speeding up

•A negative slope means an object is slowing down

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25

0

20

40

60

80

100

120

0 1 2 3 4 5 6 7 8 9

Time (sec)

Dis

tan

ce (

m)

What’s Going on?

Constant Velocity

at rest (0 velocity)

Negative velocity (backwards)

Acceleration