Chapter 2- Motion in 1 dimension

Types of motion Translation - moving along a path (straight or curved) Rotation - rotating head over feet

How can you tell if something is in motion? It is changing position How can you tell if something is changing position Is my desk moving?

Note solar system not to scale

Our approximate location in the Milky Way Galaxy

Our “local group” of galaxies

The motion of an object must be judged relative to a reference point. 55 Compared to the sign the car is moving

By need, we unconsciously judge the motion of an object as COMPARED to something else. example: You have your foot on the brake but the car next to rolls back

If you were in a spaceship with nothing in site, could you devise an experiment to determine if you were in motion (at a constant speed) or if you were stationary? NO, but you could determine if you were changing speed or direction (accelerating)

The first postulate of Einstein’s Special Theory of relativity, is that there is no stationary reference point in the universe by which to to judge the motion of other object. A reference point must be chosen, and the choice is arbitrary. One frame of reference is not better than another with the exception of convenience.

Relative Motion Applet What would be different if you were stationary and everything was moving toward you?

Frame of reference- Its all relative When describing motion, you must choose an object or point to judge by A BC Train is moving 50 m/s D 3 m/s 5 m/s What is the relative speed between A & B A & D B & C B & D A & C C & D 50 m/s 3 m/s 53 m/s 45 m/s 5 m/s 8 m/s

There are many different ways to represent motion Words Pictures Equations Graphs

Describing motion How could you describe the motion of an object? SPEED

Describing motion How could you describe the motion of an object? Direction

Describing motion How could you describe the motion of an object? Speeding up, slowing down, constant speed

Describing motion How could you describe the motion of an object? Straight Line Path Turning

We will look translation in 1 dimension 1 st y x

Displacement: The straight line distance and direction from the starting position to the final position.

When dealing with motion on the x-axis (horizontal) the following notation is used 0 m 10 m20 m30 m40 m 50 m60 m70 m80 m90 m100 m x StartFinish x1x1 x2x2  x = x 2 - x 1 Displacement =

Other common notation used 0 m 10 m20 m30 m40 m 50 m60 m70 m80 m90 m100 m x StartFinish xixi xfxf  x = x f - x i Displacement =

Other common notation used 0 m 10 m20 m30 m40 m 50 m60 m70 m80 m90 m100 m x StartFinish xoxo x  x = x – x 0 Displacement =

The FINAL POSITION (in the x axis) is referred to as 0 m 10 m20 m30 m40 m 50 m60 m70 m80 m90 m100 m x StartFinish x o =0 mx =x =40 m

0 m 10 m20 m30 m40 m 50 m60 m70 m80 m90 m100 m x StartFinish  x = x 2 - x 1 Displacement = Will the displacement be + or – 40 m? ORDER COUNTS!! -40 m

0 m 10 m20 m30 m40 m 50 m60 m70 m80 m90 m100 m x StartFinish The sign on the number indicates DIRECTION ORDER COUNTS!!  x = + 40 m A 40 m change in the positive x direction!!

0 m 10 m20 m30 m40 m 50 m60 m70 m80 m90 m100 m x StartFinish What is the displacement? ORDER COUNTS!!  x = 50 m – 80 m = - 30 m

Often the standard Cartesian coordinate system is used. +y +x-x -y But you can choose to flip them for convenience, if you are consistent.

+y +x-x -y But you can choose to flip them for convenience, if you are consistent. I’ll show you what I mean. You can even move around the origin.

0 m10 m20 m30 m40 m 50 m60 m StartFinish -10 m-20 m-30 m -40 m  x = 30 m – 0 m = + 30 m Where is the origin, and what is the positive x direction? + x

0 m10 m20 m30 m40 m 50 m60 m StartFinish -10 m-20 m-30 m -40 m  x = 30 m – 0 m = + 30 m 0 m10 m20 m30 m40 m50 m 60 m Start Finish Where is the origin, and what is the positive x direction? + x 70 m 80 m90 m -10 m  x = 20 m – 50 m = - 30 m

If you get to pick (instead of me or the book) Usually you will pick the starting point as “0” & The positive direction as the direction of motion x 0 m 10 m-10 m start Increasing X

Changing the coordinate system -50 m -40 m-30 m-20 m-10 m 0 m10 m20 m30 m40 m50 m x Start Finish Displacement =-20 m - 0 m = -20 m

Changing the coordinate system 100 m 90 m80 m70 m60 m 50 m40 m30 m20 m10 m0 m x Start Finish Displacement =70 m - 30 m = 40 m In this system, a positive vector indicates moving to the left

In this system is a positive displacement moving left or right? -100 m -90 m-80 m-70 m-60 m -50 m-40 m-30 m-20 m-10 m-0 m x Displacement =-30 m - (-50 m) = 20 m Start Finish In this system, a positive vector indicates moving to the Right (the numbers get bigger to the right)

-50 m -40 m-30 m-20 m-10 m 0 m10 m20 m30 m40 m50 m Start Finish Displacement = -10 m – (-30) m = +20 m  y = y 2 – y 1 Moving in the Y axis

Displacement and Distance have different meanings. Distance: the total path length traveled Displacement: The distance and direction from the starting position to the final position.

Distance vs Displacement Distance - the total distance traveled Displacement - the distance between the starting and ending point start Finish

You leave your home to shop and upon your return, your odometer reads 5.2 miles more than when you left. Sprawl-Mart What is the distance and displacement for your trip?

A dragon flies in a straight line for 5 km. What is the distance and displacement? Both 5 km

Find the distance and displacement 0 m 10 m20 m30 m40 m 50 m60 m70 m80 m90 m100 m x StartFinish Displacement =30 m - 60 m = - 30 m The negative sign indicates movement to the left on this system

Find the distance and displacement 0 m 10 m20 m30 m40 m 50 m60 m70 m80 m90 m100 m x Start Finish Displacement =60 m - 20 m = +40 m displacement Is distance the same? Distance =80 m + 40 m = 120 m

Find the distance and displacement 0 m 10 m20 m30 m40 m 50 m60 m70 m80 m90 m100 m x Start Finish Displacement =50 m - 90 m = -40 m displacement Is distance the same? Distance =80 m + 40 m = 120 m

Looking for direction? VECTORS

Scalar - just indicates magnitude Measurements or calculations come in two basic flavors Vectors - indicates magnitude and direction 30 cm55 mph65 kg 35 knots S-SW 35 mph West65 km North

Which would not make sense as a vector? (having a direction associated with it) Displacement Mass Temperature Velocity Time Force

Vectors can be represented using text or straight arrow.  X = +5.0 m 5.0 m East 5.0 m They all give you the same info!

Why use an arrow instead of a straight line? 5.0 m

Vectors The length indicates the magnitude Scale: 1 cm = 5 m The vectors have the same direction but different magnitudes

Vectors The arrowhead tells the direction Scale: 1 cm = 5 m The vectors have the same magnitude but different directions

If you want to show that a variable is a vector you can F F Have an arrow above it be in bold (I usually don’t do this on the board, because it is understood that certain things are vectors) or

DistanceDisplacement startFinish Which could be represented by a vector?

Does the line indicate distance or displacement? distance displacement

If you wanted to determine the speed of a runner on a road, what equipment would you need? ( a radar gun is not allowed) Speed = distance time

Average Velocity v avg = displacement time velocity is similar to speed but …. Don’t need to write this down Uses displacement Is a vector Uses distance Is a scalar

Average Velocity v = xx tt v avg = displacement time Common shorthand for average is to put a line over it. v is pronounced “v bar”

v = xx tt x 2 -x 1 t 2 -t 1 Mental Note: This is shorthand…. for this.

velocity = displacement time Speed = distance time (speed & distance do not indicate direction)

A runner travels around a m track in 40.0 seconds. What is their average speed & average velocity? s = 10.0 m/s v = 0 m/s

Velocity will have the same direction as displacement Will the velocity be positive or negative? 0 m 10 m20 m30 m40 m 50 m60 m70 m80 m90 m100 m x Start Positive

Velocity will have the same direction as displacement Will the velocity be positive or negative? -50 m -40 m-30 m-20 m-10 m 0 m10 m20 m30 m40 m50 m x Start What is the velocity if the displacement occurred over 10.2 s

Velocity will have the same direction as displacement Will the velocity be positive or negative? -50 m -40 m-30 m-20 m-10 m 0 m10 m20 m30 m40 m50 m x What is the average velocity if the distance was traveled in 40 s?

-100 m -90 m-80 m-70 m-60 m -50 m-40 m-30 m-20 m-10 m-0 m x Will the velocity be positive or negative? Positive

What is the displacement of a car which drives with an average velocity of 23 m/s east for 15 seconds? Why was this likely only the average velocity?

A boat travels at +15 km/hr for 30 km and then at +20 km/hr for another 80 km. What was the average velocity for the entire trip?

Using relative speed / velocity

Two cars are 100 km away from each other. What is their relative speed? 35 km/hr 65 km/hr 100 km relative distance

Two cars are 100 km away from each other. When do they crash 35 km/hr 65 km/hr 100 km After 1 hour 35 km65 km

The same as if one car was still and the other had the relative speed 0 km/hr 100 km/hr 100 km

If two cars are pointed at each other. Car one is traveling at 12.3 m/s E and car two is traveling at 24 m/s W. If they are initially 895 m apart. How long will it take for them to crash. What is each car’s displacement (don’t forget direction).

Two cars are 100 km away from each other. What is the relative speed between them 30 km/hr 80 km/hr 100 km

Two cars are 100 km away from each other. When do they crash? 30 km/hr 80 km/hr 100 km

Hour Hours

You have a collection of marbles, ranging from small (100 g) to big (500 g). If the average mass is 300 g, how many marble in the collection will have a mass of 300 g? An average leaves a lot of information out!!

0.0 m10.0 m You race a friend to the wall in 2.0 seconds. What was your average velocity? 5.0 m/s E East

0.0 m10.0 m You race a friend to a wall in 2.0 seconds. Your average velocity is 5.0 m/s E East v = Why is this only an average?

Why is it just average? A student hops in their car and drives east on the interstate. (We will call East the positive x direction) They arrive 51 miles away 1.5 hours later? The minimum speed limit is 40 miles an hour. Did they get a ticket for going too slow? 0 miles 51 miles Time - 0 hr Time hr v = 34 mi hr

0 miles 51 miles Time - 0 hr Time hr mi hr No, they just stopped for lunch along the way is just the average. They could have been driving 90 mph before and after lunch. 34

Average velocity = x x t t Instantaneous velocity: your speed at a given moment in time

What does a speedometer tell you? Average Speed or Instantaneous Speed

A car finishes a m run in 4.85 seconds. Can you find the average velocity or the instantaneous velocity? Is this average or instantaneous?

Read 2-2 & 2-3 Do WS 2.1

Using Pictures and Graphs to describe more than the average velocity. (what goes on between the and finish) ??

Motion Graphs are a way of showing what happens between the start and finish. It is like the wall at the magic house (sort of). Pictures are taken at a CONSTANT TIME INTERVAL

What is the average velocity of the runner between “frames” if the time interval is 0.5 seconds? 0 m1 m2 m3 m4 m

What is the average velocity of the runner for the entire 4 m run? (taking 2 seconds) 0 m1 m2 m3 m4 m

What happens to the instantaneous velocity of the runner during the run? 0 m1 m2 m3 m4 m

0 m1 m2 m3 m4 m If an object moves at a constant velocity, then the average velocity is also the instantaneous velocity at any point

If the time interval is the same what is different between the two velocities? 0 m1 m2 m3 m4 m

One travels a greater distance in the same amount of time. 0 m1 m2 m3 m4 m

What is happening to the speed?

Instead of Pictures we can also use…. What does this one tell you???

m 50 A motion “graph” of a car. What would it look like if it were actually graphed?

m 50

If the velocity is CONSTANT, then the graph is a straight line. Why?

What is the average velocity of the car over 100 seconds? Does it change? v = xx tt displacement -not change in x on the graph (sorry about the confusion)

v = xx tt What is the displacement after 100 s? = 60 s – 0 s

v = xx tt What is the change in time for this? = 0.6 m/s 60 m – 0 m 100 s – 0 s =

v = xx tt = 0.6 m/s 60 m – 0 m 100 s – 0 s = Rise Run MAKE THE CONNECTION!!!!!!!

The slope of a displacement vs. time graph is the velocity of the object

What would be different if the object was moving twice as fast.

Who is moving faster Blue or Green Green– The bigger the slope, the bigger the velocity!! 4 m 10 s =0.4 m/s 13 m 10 s = 1.3 m/s

What is the velocity (slope) indicated?

What is the velocity? What is the object doing?

The graph represents 2 cars on a track. What does it mean & what does the intersection of the 2 lines represent?

Interpret the graph

What happened here?

Which object is moving faster?

Interpret the graph What happens to the slope of the curve? Compare the distance traveled in the first 10 seconds vs. the last 10 seconds.

What type of motion does this graph depict? & what direction 4.8 m/s 0.6 m/s 0.1 m/s Slowing DOWNPositive Velocity

4.8 m/s 0.6 m/s 0.1 m/s Are these velocities Average or Instantaneous Average over the time (run) in the slope

4.8 m/s This is still the average velocity over the 10 seconds, because the velocity changes over the 10 seconds. How do we know the velocity changes? The line CURVES

To find the instantaneous velocity at say 10 seconds. We would need to know the slope at THAT POINT. We could shrink our time frame used until it is only at that point

The INSTANTANEOUS Velocity at a time, is the SLOPE of a TANGENT LINE at that point.

Notice what happens to the slope of the tangent lines…

Applet: sports car showing instantaneous velocity as the slope of the tangent line. (bottom of page) Note no link??

Find the instantaneous velocity of the car at 30 seconds.

Car “A” Car “B” Describe the scenario Car “A” starts out in front of “B” and moves at a constant speed Car “B” accelerates and overtakes “A”

Car “A” Car “B” Describe the scenario Car “A” starts out in front of “B” and moves at a constant speed Car “B” accelerates and then decelerates to runs along side “A” Car “A” Car “B”

Car “A” Car “B” Car “A” Car “B” Where is car “B” moving the fastest?

Read section 2-4 Do WS 2.2

Now what is Acceleration If you accelerate, you change your velocity. How could you change your velocity? Speeding up Slowing down Changing Direction Is acceleration a vector?

Going from 25 mph to 55 mph? Going from 55 mph to 0 mph? Changing direction to the east at a constant speed IS THIS ACCELERATION?

Average acceleration a = vv tt v 2 -v 1 t 2 -t 1 a = Acceleration is rate at which you change velocity!!!

vv tt a = What are possible units of acceleration s m s 1 s 1 s x m s2s2 =

If an object initially at rest experiences a constant acceleration of +6 m/s 2. Time (s) Velocity (m/s)

If an object initially moving at 10 m/s experiences a constant acceleration of 4 m/s 2. Time (s) Velocity (m/s)

Two race cars start from a dead stop. Car 1 Reaches a speed of 51 m/s in 5.6 s Car 2 Reaches a speed of 59 m/s in 5.6 s Which car had the greater acceleration?

In another race, two race cars start from a dead stop. Car 1 Reaches a speed of 51 m/s in 4.3 s Car 2 Reaches a speed of 51 m/s in 4.8 s Which car had the greater acceleration?

The Porshe Boxster can reach 97 km/h from rest in 4.6 seconds. What is its average acceleration.

A car is moving at 58 m/s when it opens its chute and comes to a stop 38 seconds later. What is the acceleration during this time? a = v 2 -v 1 t 2 -t = m s 0 m s s0 s = -1.5 m s2s2 Why negative???

An object accelerates speeds up slows down changes direction DUE TO A FORCE. An object will accelerate in the same direction as that of the applied force!

m velocity The velocity is positive Positive acceleration will cause The car to speed up Negative acceleration will cause The car to slow down Positive acceleration Negative acceleration

m The velocity is negative Positive acceleration will cause The car to speed upNegative acceleration will cause The car to slow down velocity Positive acceleration Negative acceleration

x m Positive acceleration x m Positive acceleration Two cars are initially stopped, the show positive acceleration. Which way to they move?

If an object initially moving at +10 m/s experiences a constant acceleration of -5 m/s 2. Time (s) Velocity (m/s)

What will happen to an object with a positive velocity, if it continues to negatively accelerate. It will slow down, then… It will STOP, then… Go backwards, then…

A car initially is moving at 5.6 m/s. It accelerates at a rate of -1.1 m/s 2 for 6.0 seconds. What is its final velocity?

A car travels a constant 35 m/s for 7.0 seconds. What is its acceleration?

Displacement vs Time graph review ( with signs)

What is the sign (+ -) for the depicted: Velocity? Acceleration?

What does the Y- Intercept mean here???

What type of motion does this graph depict? & what direction Forward, Slowing DOWN Positive Velocity Which means the acceleration is… negative

What is the sign (+ -) for the depicted: Velocity? Acceleration?

What type of motion does this graph depict? & what direction? Speeding up Negative velocity Which means the acceleration is… negative

What type of motion does this graph depict? Speeding uppositive velocity Which means the acceleration is… positive

What type of motion does this graph depict? Constant positive velocity stopped Which means the acceleration is… But the overall acceleration is negative Zero acceleration here

What type of motion does this graph depict? Constant negative velocity Constant positive velocity What about the overall acceleration?

What type of motion does this graph depict? Slowing positive velocity stopped Speeding up negative velocity

Applets for graphs 2.1,2.2 Exploration 2.1, 2.2 Problems 2.1

Read 2-5 Do problems page 43 #’s 13,14 13 is 4.3 m/s 2 14 is 5.2 s Note for next year do 1 st 3 problems on 2.3