LINEAR MOTION

FAST

Speed•depends on distance and time

Average speed•uses total distance and total time•Use this when an object travels at different speeds

SCALARS VS. VECTORS•Scalars: measure the amount (magnitude)•ex:

•distance traveled• temperature•speed limits

•Vectors: measure both amount and direction•vector: scalar with a direction•ex:

•velocity of a car•weight

Vector or Scalar? Categorize each quantity as being either a vector or a scalar. Category Quantity

a. ___________________ 5 mb. ___________________ 30 m/s Eastc. ___________________ 10 mi. Northd. ___________________ 20 degrees Celsiuse. ___________________ 256 Megabytesf. ___________________ 4000 Calories

Scalar

ScalarScalarScalar

VectorVector

DISTANCE VS. DISPLACEMENT•distance: total miles traveled (scalar)

•displacement: change in position (vector)•distance from start to end

2a. What is the displacement and distance of runners when they finish a one-mile race on an oval track?Distanc

e: Displacement:

1 mi0 mi

DISTANCE VS. DISPLACEMENT•distance: total miles traveled (scalar)

•displacement: change in position (vector)•distance from start to end

2b. What is your displacement and distance if you walk 3m north and then 5m south? Distanc

e: Displacement:

3m + 5m = 8m 3m - 5m = 2m

south

3m 5m

SPEED VS. VELOCITY

•Speed ( v ) = distance / time•Velocity ( ) = displacement / time

arrows mean they are vectors

distance

displacement

Time to PracticeGo to pg. 248

Complete Problems #3-5

Work ahead! #6-8

REFERENCE FRAMES•Speed is Relative•R.F. allow you to compare speeds•How fast are you moving now?•Earth is rotating at 1,000 mph

FRAME OF REFERENCE•Earth is orbiting sun at 66,000 mph•Everything in universe is moving

FRAME OF REFERENCE•Lets say you are on a train moving 40 mph •If you walk towards the front of the train at 5 mph, you are going 5 mph relative to the train

1. What is your speed relative to someone standing by the train tracks? 5 mph 40 mph

45 mph

FRAME OF REFERENCE•Lets say you are on a train moving 40 mph

2. What is your speed relative to someone standing by the train tracks if you walk towards the back of the train at 5 mph?

5 mph40

mph35 mph

FRAME OF REFERENCE•Is this car moving?

•Speed Limit of the Universe: light speed! (3.0 x 108 m/s)

Time to PracticeGo to pg. 248

GRAPHING RULES

1. Use a ruler (straightedge)!

2. Label your axes!• (units in parentheses)

• time is always the x-axis

Time (s)

Variable

Unit

Distance (m)

GRAPHING RULES

3.Title the graph!

(Y vs. X)

Distance vs. Time

Time (s)

Distance (m)

GRAPHING RULES

4.SCALE. Stretch out your

axes!

GRAPHING RULES5. Use a Pencil!!6. Do not just connect the dots!

Line of best fit curve: smooth line: ruler

The line might not touch dots

GRAPHING RULESDrawing tangent

linesdrawn at a point“balance” ruler on

curve perpendicular with

normal

Distance vs. Time

Time (s)

Dist

ance

(m

) make it long enough to find the slope

Ahh. Just right!

GRAPHING: START WORK! PG 254

Time (s)

Dist

ance

(m)

(0.15, y1)(x2, y2)

Distance vs. Time

0.15 s

MOVIES

And now for a short movie

EUREKA: INERTIA – 1:25

EUREKA: MASS -- BROKEN

EUREKA: SPEED -- BROKEN

ACCELERATION•acceleration the rate of change of velocity

• = final velocity• = initial velocity•refers to speeding up and slowing down or…

arrows mean …

Velocity

Speed Direction

EXAMPLEA car moving at 20 m/s comes to a stop in four seconds. What was the car’s acceleration?

Given:

Unknown:

EXAMPLE

solve for acceleration

said “negative five meters per second per second”negative acceleration means… slowing down

ACCELERATION•You “feel” speed when you accelerate•This includes speeding up, slowing down and

• sharp turns at constant speed!•All three are accelerations

EUREKA: ACCELERATION I

EUREKA: ACCELERATION II

Start Homework!

DISTANCE VS. TIME GRAPHS

•Slope

•units are

• the slope is velocity!

Increasing Speed

Time (s)Dist

ance

(m)

Time (s)Di

stan

ce (m

)

Constant speed

SPEED VS. TIME GRAPHS

•Slope

•units are

• the slope is acceleration!

Speed vs. Time Graphs

speed acceleration

Distance traveled

1. Find the instantaneous acceleration at Points a, b, and c

Points a

Point b

Point c t

v

Velocit y T ime Gr aph

a

b

1 2 3 4 5

c

1

2

3

42 m/s2 (speeding up)

0 (traveling at constant speed)

-1 m/s2 (slowing down)

2. Use the graph below to find the velocity from:

i. start to a

ii. a to b

iii. c to d

iv. What is displacement after 9 sec?

x m/s

t

x

Pos it ion T ime Gr aph

ab

5

5

10 15

c

5

d

e

FREEFALL• freefall objects moving under only force of gravity

• due to gravity = g•g = 9.8 m/s2

•Terminal velocity is the fastest an object can fall• terminal velocity when air resistance becomes equal to gravity

FREEFALL• let’s look at the motion of three objects

•An object dropped from rest•An object thrown downwards•An object thrown upwards

All have the same acceleration!

•All of these motions are types of…freefall!

EUREKA: GRAVITY

LAB: Acceleration due to Gravity pg. 270-273

1. Make sure the motion detector only “sees” the ballNot your 3rd arm or extra headNot a table or the wire basket2. Cover the motion detector

with a wire basket• Throw the ball up and

catch it3. Throw the ball after you hear faster beeps

LAB: Acceleration due to Gravity pg. 270-273

1. Make sure your graph makes sense• Optional: zoom in on the important stuff

2. Plot your line of best fit (it should be linear)3. Once you are ready to print your graphs:

• Plug your LabQuest into the printer • Click File Print graph• On a Sticky Note write:

• your name and # of copies needed • stick it to your 2 graphs

4. Record your data on your data table• Optional: save your data to a USB

Don’t forget to….

READ THE INSTRUCTIONS VERY CAREFULLY.

Complete your data table before you erase your data

1. Label your axis: variable & units

2. Title your graph: _____ vs. _____

Lab Questions

Displacement, Velocity & acceleration graphs: http://www.youtube.com/watch?v=_ES1JJ7ErzI

Slow Motion Ball: http://www.youtube.com/watch?v=1PyjLXIYMzI&feature=related

PUTTING IT TOGETHER•Let’s use what we know about graphs to make two more formulas.

•Let’s look at the graph from ti to tf

PUTTING IT TOGETHER•Each time matches up with a

velocity• Initial velocity is vi •final velocity is vf

v iv f

PUTTING IT TOGETHER•To find distance:• area between the line and the x-axis

•d = area of rectangle + area of trianglev i

v f

PUTTING IT TOGETHER•d = area of rectangle + area of triangle

•area of rectangle =•area of triangle =

v iv f

PUTTING IT TOGETHER

we now have a connection between a and d

PUTTING IT TOGETHER•solve for t from first a equation•substitute into second a equation•a little fancy algebra and…

nice if you do not have t

PUTTING IT TOGETHER

•use equation 1 only if acceleration is zero

•use equations 2-4 only if constant acceleration

PUTTING IT TOGETHER

•notice there are no arrows•However, the variable are ALL still vectors

PUTTING IT TOGETHER

•vectors mean that direction is important•ex. positive represents up, negative for down

EXAMPLEA spear is thrown down at 15 m/s from the top of a bridge at a fish swimming along the surface below. If the bridge is 55 m above the water, how long does the fish have before it gets stuck?

-15m/s-55m-9.8m/s2

start

end

x

y

EXAMPLEA spear is thrown down at 15 m/s from the top of a bridge at a fish swimming along the surface below. If the bridge is 55 m above the water, how long does the fish have before it gets stuck?

Given:

Unknown:

why negative?

EQUATION

Which equation has vo, d, a and t?• This works, but…you would need to use the quadratic formula & pick the answer that makes sense!

• OR we could use 2 equations

EXAMPLEFirst, eqn. 4

positive or negative?

x

y

EXAMPLE• solve for t in eqn 2.• substitute vf into eqn 2.

POPPER LABETTE!Pg 278-279

* It is easier to avoid using quadratic equations in your calculations… (look @

CN)

x

y

Grading system Givens Unknown Equation Units Box

FIND THE MISTAKE(S)A ball is thrown up. It rises to a height of 1m before falling down.

x

y

start

end

vi = 0 m/s

vf = 0 m/s

FIND THE MISTAKE(S)A ball is thrown up. It rises to a height of 1m before falling down.

x

y

start

end

vi = 0 m/s

vf = 0 m/s

FIND THE MISTAKES2. Calculate how fast the popper is moving

after 0.20 s

x

yThe popper may NOT be at the top of it’s

jump!d is unknown when t

= 0.20 s