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Part A: New Symbols and Quantities / Vector Algebra Δ – delta The Greek letter that means change in physics. (note: Don’t call it “triangle”) Δv – change in velocity This is the change in your velocity. ∆𝑣 = 𝑣! − 𝑣! A.1 I begin with a velocity of 20 miles per hour, and I accelerate to a velocity of 50 miles per hour. What is my change in velocity (Δv)? A.2 I am walking with a velocity of 2.5 m/s. I realize I am late for class, so I start running at a velocity of 6 m/s. What is my change in velocity (Δv)? A.3 I am driving on the highway with a velocity of 65 miles per hour. I go off onto a side street and decelerate to 30 miles per hour. What is my change in velocity (Δv)? d (distance) vs. Δx (displacement/change in position) Distance is how far you move total. Displacement is how for you are from where you started. If you only more forward, there is no difference. If you travel forward and back, then there is a difference. A.4 Which quantity tells how far you move in total? A.5 Which quantity tells how far you move from where you started? A.6 Why is there a Δ in the symbol for displacement? (hint: look at the other name for displacement)

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Note: The kinematic equations we are going to use have displacement, not distance. This won’t make a difference as long as we deal with only forward motion. Once we reach problems where things go and come back, it will make a big difference. Direction of Displacement (Δx) Displacement has a direction, which is represented by the sign. If displacement is POSITIVE, that means you have moved forwards. If displacement is NEGATIVE, that means you have moved backwards. Speed vs. velocity Velocity is speed with direction. Direction is represented by the sign of velocity. If velocity is POSITIVE, that means you are moving forwards. If velocity is NEGATIVE, that means you are moving backwards. Direction of Acceleration: Acceleration has direction, represented by the sign. If acceleration is POSITIVE, that means you are moving faster. If acceleration is NEGATIVE, that means you are moving slower. A.7 In physics, a VECTOR is a quantity that has direction. Which three quantities in this unit are vectors? A.8 In an algebraic equation, how do we represent the direction of a vector?

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Part B: Review of Formula from Motion Equations 1

𝑎 = !!!!!∆!

𝑎 = ∆!∆!

∆𝑣 = 𝑣! − 𝑣! g = 9.8 m/s2 𝑣! = 𝑣! + 𝑎 ∙ ∆𝑡 𝑑 = average speed ∙ ∆𝑡 ∆𝑥 = 𝑣 ∙ ∆𝑡 Quantity Symbol Unit Acceleration

a

m/s2

Initial velocity

vi

m/s

Final velocity

vf

m/s

Change in velocity

Δv

m/s

Distance

d

meters (m)

Average speed

𝑣

m/s

Note: I am writing it out so it isn’t confused with velocity

Average velocity

𝑣

m/s

Time interval

Δt

Seconds (s)

Free Fall Acceleration

g

m/s2

Note: during free-fall, acceleration is 9.8 m/s2.

B.1 The world record of the 100 meter dash is 9.58 seconds (by Usain Bolt in 2009). What is his average speed in this race? Looking For

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B.2 In the Rio Olympics, Almaz Ayana of Ethiopia set a stunning world record of 29 minutes, 17 seconds [which is 1757 seconds] in the 10,000 meter run. She smashed the previous record, which had stood since 1993. What was her average speed in meters per second? Looking For

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Answer as equation with unit: B.3 In the Rio Olympics Katie Ledecky swam to a world record of 8 minutes, 4.79 seconds [which is 484.79 seconds] in the 800 meter freestyle. What is her average speed in meters per second? Looking For

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Answer as equation with unit: B.4 The Porsche 918 Spyder is capable of accelerating from rest to 27.78 m/s in a time of 2.2 seconds. What is the acceleration of the Porsche Spyder? (hint: always make sure that you use an SI unit!) Looking For

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B.5 I am driving at a velocity of 6.7 m/s. I accelerate at a rate of 3.4 m/s2 for a time of 2 seconds. What will be my final velocity? Looking For

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Answer as equation with unit: B.6 I am driving, and I begin accelerating at a rate of 2.8 m/s2 for a time of 4 seconds. After accelerating, my velocity is 14.2 m/s. What was my initial velocity? Looking For

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Answer as equation with unit: B.7 I accelerate from a speed of 3 m/s to 9 m/s, with an acceleration of 0.2 m/s2. How long does this acceleration take? Looking For

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Answer as equation with unit: B.8 I drive at a speed of 55 miles per hour for an hour and a half. How far would I travel in miles? Looking For

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Part C: Introducing the 4 Kinematic Equations Thus far, we only know how to calculate distance if something moves at a constant velocity. However, most interesting things do not move at a constant velocity, they accelerate. There are 4 equations Kinematics The study of how things move. 4 kinematic equations These are four important equations that demonstrate how things move in physics. Condition for the kinematic equations You can use the kinematic equations when ever anything is moving with a constant acceleration. If acceleration is changing, you CANNOT use the kinematic equations. Name Equation

Definition of Acceleration

𝑣! = 𝑣! + 𝑎 ∙ ∆𝑡

The King of Kinematic Equations

∆𝑥 = 𝑣! ∙ ∆𝑡 +12𝑎 ∆𝑡 !

The Average Velocity Formula

Δ𝑥 =𝑣! + 𝑣!2 Δ𝑡

No-Time Equation

𝑣!! = 𝑣!! + 2𝑎 ∙ ∆𝑥

C.1 The study of motion is called _________________________. C.2 Which kinematic equation have we already studied? C.3 True or false: If my acceleration is changing, I can use the No-Time Equation. C.4 True or false: If my acceleration is not changing, I can use The Other Average Velocity Formula.

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Part D: The King of Kinematic Equations (The Most Commonly Used Equation)

∆𝑥 = 𝑣!∆𝑡 +12𝑎 ∆𝑡 !

Symbol Quantity SI unit

∆𝑥 Displacement meters 𝑣! Initial

velocity m/s

𝑎 Acceleration m/s2

∆𝑡 Change in time, time interval

seconds

D.1a I begin at rest at the top of a cliff, and I fall down from the cliff (my acceleration is 9.8 m/s2). How far will I have gone after 3 seconds? Looking For

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Answer as equation with unit: D.1b How far will I have gone after five seconds (if it is a very tall cliff)? Looking For

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D.2 A squirrel is running with a speed of 4 m/s, and it begins accelerating at a rate of 0.3 m/s2 for 2.5 seconds. How far does it move in this time? Looking For

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Answer as equation with unit: D.3 You want to see how deep an old water well is. You drop a rock down the well. The rock is not moving before you drop it. What was the acceleration of the rock? [remember from before] If you here the rock splash into water after 4.5 seconds, then how deep is the well? Looking For

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Answer as equation with unit: D.4 A car is traveling at 23 m/s. The driver sees a deer that is 60 meters ahead and begins to slow down. If it takes the car 4 seconds to stop, what must be the acceleration so that the driver does not hit the deer? Looking For

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D.5.Someoneacceleratesatarateof5.0m/s2foratimeof10.secondsandmovesforwardadistanceof600meters.Whatwastheirinitialvelocity?Looking For

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Answer as equation with unit: D.6Someoneacceleratesatarateof5.0m/s2foratimeof10.secondsandmovesadisplacementof150meters.Whatishisinitialvelocity?Looking For

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Answer as equation with unit: Wow,theanswerisnegative!Whatdoyouthinkthatmeans?D.7TheCherryandWebbbuildingisabout20.0meterstall.IfyoudroparockfromrestofftheCherryandWebbbuilding,howmuchtimewillittakeittohittheground?Looking For

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Part E: The Average Velocity Equation This is another equation for average velocity that applies whenever acceleration is constant:

average velocity = 𝑣! + 𝑣!2

E.1 What is the average of 5, 12, and 19? E.2 What is the average of 3, 8, 10, and 11? E.3 Explain how to calculate the average in mathematics. E.4 Now, explain the average velocity formula written above. How does make sense? The formula:

Δ𝑥 =𝑣! + 𝑣!2 Δ𝑡

E.5 Where does this formula come from? (Hint: look at the formulas you used in part B). Symbol Quantity SI Unit

∆𝑥 displacement, change in position

m

𝑣! initial velocity m/s 𝑣! final velocity m/s ∆𝑡 time interval s

Common usage: This formula is often used for things that are starting or stopping.

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E.6 A squirrel running at 3 m/s accelerates to 5 m/s in 0.5 seconds. How far does he move while accelerating? Looking For

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Answer as equation with unit: E.7 A car begins at rest. Over the course of 5 seconds, it accelerates to 25 m/s. In this time, how far does it move? Looking For

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Answer as equation with unit: E.8 A car is shooting down the highway at 19 m/s. He sees a deer 60 m ahead, and slams the brakes. It takes 5 seconds to stop. How far does he move while stopping? Looking For

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Answer as equation with unit: Does he hit the deer?

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E.9 A car decelerates from 25 m/s to 15 m/s in 40 seconds. How far does it travel during this time? Looking For

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Answer as equation with unit: E.10Somebodytravelsforatimeof20.secondsandmovesadisplacementof300.meters.Theirfinalvelocityis18m/s.Whatwastheirinitialvelocity?Looking For

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Answer as equation with unit: E.11Somebodyistraveling5m/stotheright.Theymoveataconstantaccelerationandenduptravelingat5m/stotheleft.Youdonotknowtheirtimeoracceleration.Whatistheirdisplacement?[hint:ThinkabouttheinformationyouDOknowandusetheequationabove]Looking For

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Answer as equation with unit:

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Part F: The no-time formula

𝑣!! = 𝑣!! + 2𝑎 ∙ ∆𝑥 Symbol Quantity SI Unit

∆𝑥 displacement, change in position

m

𝑣! initial velocity m/s 𝑣! final velocity m/s 𝑎 acceleration m/s2

F.1 What does PEMDAS stand for? F.2 What does PEMDAS mean? F.3 A running dog has an acceleration of 2 m/s2, and accelerates from an initial speed of 5 m/s. If he moves 20 meters while accelerating, what is his final speed? [NOTE: at the end, you need to use a square root to find your answer.] Looking For

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Answer as equation with unit: F.4 A car accelerates from rest with an acceleration of 3 m/s2. If it moves 100 m while accelerating, what is its final speed? Looking For

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F.5 A running dog accelerates from 4 m/s to 8 m/s. He has an acceleration of 3 m/s2. How far does he move while accelerating? Looking For

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Answer as equation with unit: F.6 Help! You just fell straight down a well. Your acceleration is 9.8 m/s2. The well is 30 meters deep. How fast are you traveling when you hit the bottom of the well? Looking For

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Answer as equation with unit: F.7 A driver sees a kid on the road in front of him. He slams his brakes, but ends up hitting the child. Afterwards, the driver claims that he was driving very safety and not speeding at all. A police detective decides to inspect if he is telling the truth. He knows from examining the crash that the car hit the kid at 4 m/s. He looks at the tire marks on the road and sees that the car moved 60 m after he hit the brakes. He looks up vehicle information and sees that his car could decelerate at -3 m/s2. What was the car’s velocity BEFORE he started slowing down? Looking For

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Answer as equation with unit: If the speed limit on that road was 35 mph (16 m/s), was the car speeding?

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Answers A.1 Δv = 30 m/s A.2 Δv = 3.5 m/s A.3 Δv = 35 mph A.4 distance A.5 displacement A.6 Because displacement is change in position, and the Δ stands for change A.7 displacement, velocity, acceleration A.8 with the sign; + indicates one direction, and – indicates the other direction B.1 v = 10.2 m/s B.2 v = 5.69 m/s B.3 v = 1.65 m/s B.4 a = 12.63 m/s2 B.5 vf = 13.5 m/s B.6 vi = 3 m/s B.7 Δt = 30 s B.8 d = 82.5 m C.1 kinematics C.2 The Definition of Acceleration C.3 False C.4 True D.1a Δx = 44.1 m D.1b Δx = 122.5 m D.2 Δx = 10.94 m D.3 Δx = 99.225 m D.4 Δx = - 4 m/s2

D.5 𝑣! = 35 m/s D.6 𝑣! = −10 m/s, The initial velocity is negative he started out moving the opposite direction. D.7 ∆𝑡 = 2.02 s

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E.1 12 E.2 8 E.3 To calculate the average, you add all numbers and divide by how many numbers there are. E.4 The formula

!!!!!!

is the average of final and initial velocity.

E.5 If acceleration is constant, this formula is identical to the formula ∆𝑥 = 𝑣 ∙ ∆𝑡, displacement = (average velocity (time) E.6 Δx = 2 m E.7 Δx = 62.5 m E.8 Δx = 47.5 m, no E.9 Δx = 800 m E.10 𝑣! = 12 m/s E.11 ∆𝑥 = 0 F.1 PEMDAS = Parentheses, Exponent, Multiplication, Division, Addition, Subtraction F.2 PEMDAS gives the order that operations should be completed in a mathematical equation. F.3 vf = 10.25 m/s F.4 vf = 24.5 m/s F.5 Δx = 8m F.6 vf = 24.2 m/s F.7 vi = 19.39 m/s