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Linear Motion

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**Vocabulary Motion Distance Displacement Speed Instantaneous speed**

Average speed Velocity Acceleration Scalar Vector Free fall Elapsed time

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**What is motion? How can we tell if something has moved?**

Motion is when an object changes its position relative to a fixed point.

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**Distance vs. Displacement**

Distance: The total amount you have travelled Displacement: the distance from your start point

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**Example Jason ran a lap around the track.**

What is his displacement? What distance did he run? Sierra missed the bus and had to walk home. She lives 5 miles from school. What is her displacement? What is her distance walked?

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**But what if they change direction?**

If an object changes direction, the displacement will change If the object turns 900, to find the displacement, we must use the Pythagorean theorem Displacement Direction B Direction A

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Example Dallas ran 3 blocks east, then turned the corner and ran 2 blocks south. What is his distance? 3 + 2 =5 blocks What is his displacement? = C2 9 + 4 =13 √13 = 3.60 blocks SE

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**DISTANCE vs. DISPLACEMENT QUIZ:**

In your own words, define distance. In your own words, what is displacement? What is the total distance of a student who walks 3 blocks east, 2 blocks north, 1 block west, and then 2 blocks south? What is the student’s displacement in #3? A girl leaves a history classroom & walks 10m north to a drinking fountain. She turns & walks 30m south to an art classroom. What is the girl's total displacement from the history classroom to the art classroom? What should you do in the event of a fire in lab?

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**DISTANCE vs. DISPLACEMENT QUIZ:**

In your own words, define distance. In your own words, what is displacement? What is the total distance of a student who walks 3 blocks east, 2 blocks north, 1 block west, and then 2 blocks south? What is the student’s displacement in #3? A girl leaves a history classroom & walks 10m north to a drinking fountain. She turns & walks 30m south to an art classroom. What is the girl's total displacement from the history classroom to the art classroom? What should you do in the event of a fire in lab?

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**Speed Speed is how fast an object is moving**

Speed = distance covered/ time In a straight line, distance would be x So, s = (Dx) / (Dt) Units are distance per time Ex: mph, km/h, m/s

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Speed Instantaneous speed is how fast an object is moving at a certain time (in an instant) Ex: Speedometer in a car measures instantaneous speed

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Speed Average speed is the total distance over the total time

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**Can a player hit a ball only by knowing its speed?**

What else do you need to hit the ball? Is speed a scalar or a vector?

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**Two Types of Quantities**

Name: ___________ Block:__ Date: ___ Speed Two Types of Quantities Has _______ and ______ Example: _______ Example: ________

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**List of concepts that you need to use to complete your web.**

* 10 miles per hour * 10 miles per hour north * Velocity * Needs direction * Doesn’t need direction * Scalar quantities * Vector quantities * Has magnitude(number) only * Has magnitude and direction

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**Velocity Speed is a scalar Velocity is speed in a given direction**

Velocity is the vector of speed The equation for velocity is the same as speed: v = Dx / Dt

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**Velocity Velocity is speed in a direction**

Therefore, changing speed changes velocity Also, changing direction changes velocity

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**SPEED / VELOCITY PROBLEMS:**

EXERCISE 1: Hans stands at the rim of the Grand Canyon and yodels down to the bottom. He hears his yodel echo back from the canyon floor 5.20 s later. Assume that the speed of sound in air is m/s. How deep is the canyon at this location? s = m/s t = 5.20 s d = ? d S t

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**SPEED / VELOCITY PROBLEMS:**

EXERCISE 2: The world speed record on water was set on October 8, 1978 by Ken Warby of Blowering Dam, Australia. If Ken drove his motorboat a distance of 1000 m in s, how fast was his boat moving a) in m/s? b) in mph? s = ? t = s d = 1000 m d S t

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**SPEED / VELOCITY PROBLEMS:**

EXERCISE 3: According to the World Flying Disk Federation, the world distance record for a flying disk throw in the men’s 85-years-and-older category is held by Jack Roddick of PA, who on July 13, 2007, at the age of 86, threw a flying disk for a distance of 54.0 m. If the flying disk was thrown horizontally with a speed of 13.0 m/s, how long did the flying disk remain aloft? s = 13.0 m/s t = ? d = 54.0 m d S t

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**SPEED / VELOCITY PROBLEMS:**

EXERCISE 4: It is now 10:29AM, but when the bell rings at 10:30AM Suzette will be late for French class for the 3rd time this week. She must get from one side other school to the other by hurrying down 3 different hallways. She runs down the first hallway, a distance of 35.0 m, at a speed of 3.50 m/s. The hallway is filled with students, and she covers its 48.0 m length at an average of 1.20 m/s. The final hallway is empty, and Suzette sprints its 60.0 m length at a speed of 5.00 m/s. Does Suzette make it to class on time or does she get detention for being late again? d S t

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**SPEED / VELOCITY PROBLEMS:**

EXERCISE 6: A hiker is at the bottom of a canyon facing the canyon wall closest to her. She is meters from the wall and the sound of her voice travels at 340 m/s at that location. How long after she shouts will she hear her echo? (Be careful to consider why echoes happen.) d v t

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**Acceleration Acceleration is how fast velocity changes**

(The speed of speed) The equation for acceleration is: a = Dv / Dt Can be positive or negative or a change in direction (Acceleration is also a vector)

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**ACCELERATION PROBLEMS:**

EXERCISE 5: A jumbo jet taxiing down the runway receives word that it must return to the gate to pick up an important passenger who was late to his connecting flight. The jet is traveling at 45.0 m/s when the pilot receives the message. What is the acceleration of the plane if it takes the pilot 5.00 s to bring the plane to a halt? v = 45.0 m/s t = 5.00 s a = ? v a t

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**ACCELERATION PROBLEMS:**

EXERCISE 5: A jumbo jet taxiing down the runway receives word that it must return to the gate to pick up an important passenger who was late to his connecting flight. The jet is traveling at 45.0 m/s when the pilot receives the message. What is the acceleration of the plane if it takes the pilot 5.00 s to bring the plane to a halt? v = 45.0 m/s t = 5.00 s a = ? v a t

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**Free Fall How do objects move when they fall? Do they speed up?**

Does their speed remain constant? Do they slow down? Can you safely catch a penny dropped from 1m? Can you safely catch a penny dropped from the Empire State building?

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**Free Fall Objects accelerate (speed up) as they fall**

This acceleration is due to the force of gravity Gravity causes objects to accelerate by roughly 10m/s each second they fall

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**Table 4.2 Elapsed Time (s) Instantaneous speed (m/s) 1 10 2 20 3 30 4**

1 10 2 20 3 30 4 40 t 10t

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**Acceleration of gravity**

From this table, we see that the speed is equal to 10m/s times the time v = 10 t 10 m/s is often represented by the constant g (for gravity acceleration) So, Dv = gDt With an initial velocity, Dv = gDt +vo

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Up and Down How does the speed change if an object is thrown straight up? What forces are acting on the object? What would be it’s acceleration?

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Up and Down The vertical acceleration of any object is ~10 m/s down (g) A rising object slows down by this much each second A falling object speeds up by this much each second.

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How far does it go? Just because the instantaneous speed is 10m/s does not mean an object has fallen 10 m. It sped up from 0 to 10 in that second. Its average speed was 5 m/s [(10+0/2)] That means it did not fall 10 m.

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How far does it go? Elapsed time Distance 1 5 2 20 3 45 4 80 t ½ g t2

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How far does it fall? The distance can be determined by the equation: d = ½ g t2 Or, to put it in general terms, v = at d = ½ a t2 (These equations work for any constant acceleration and initial speed = 0) d = vot -½ g t2 if there is an initial speed

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Ch5 – Mathematical Models

Ch5 – Mathematical Models

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