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**Metric Prefixes Practice**

If a radio wave has a period of 1 µs, what is the period in seconds? A hydrogen atom has a diameter of about 10 nm. Express this diameter in meters. Express this diameter in millimeters. Express this diameter in micrometers. The distance between the sun and Earth is about 1.5 X 1011 m. Express this distance in kilometers and gigameters.

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Frame of Reference A system that defines where objects are for a problem. For certain problems, there may be multiple frames of reference that can be used.

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Scalar Vs. Vector Scalar Vector

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Displacement Similar to distance, but displacement will also include the direction traveled. Direction is indicated by a positive or negative number. Positive means right or up and negative means left or down. Equation: Δx=xf-xi Units:

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Velocity Similar to speed, but velocity also includes the direction traveled. We will calculate average velocity using the equation, 𝑉𝑎𝑣𝑔= Δ𝑥 Δ𝑡 = 𝑥𝑓−𝑥𝑖 𝑡𝑓−𝑡𝑖 The sign conventions that we used for displacement also work for velocity. Units:

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**Average Velocity Example**

During a race on level ground, Andra runs with an average velocity of 6.02 m/s east, what is her displacement after 137 s?

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**Average Velocity Problems**

Heather and Matthew walk with an average velocity of 0.98 m/s east. If it takes them 34 minutes to walk to the store, what is their displacement? If Joe rides his bicycle in a straight line for 15 minutes with an average velocity of 12.5 km/hr south, how far has he ridden?

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Problems Continued Simpson drives his car with an average velocity of 48.0 km/hr east. How long will it take him to drive 144 km on a straight road? A bus travels 280 km south along a straight path with an average velocity of 88 km/hr south. The bus stops for 24 minutes. Then, it travels 210 km south with an average velocity of 75 km/hr south. How long does the total trip last? What is the overall average velocity?

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**Instantaneous Velocity**

Instantaneous velocity can be found on a position vs. time graph. It is the velocity at a given point in time. It is found by finding the slope of the tangent line at that point of the graph. Tangent line-

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**What is the instantaneous velocity at 1s, 3s, 4.2s and 7.3s?**

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**Acceleration Defined as the rate in change of velocity**

It could be a change in speed and/or direction The following equation allows us to calculate average acceleration: 𝑎𝑎𝑣𝑔= Δ𝑣 Δ𝑡 = 𝑣𝑓−𝑣𝑖 𝑡𝑓−𝑡𝑖 Unit for acceleration:

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**Velocity and Acceleration**

vi a motion + speeding up - slowing down + or - constant velocity speeding up from rest at rest

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**Average Acceleration Example**

A shuttle bus slows down with an average acceleration of -1.8 m/s2. How long does it take the bus to slow from 9.0 m/s to a complete stop?

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**Average Acceleration Problems**

A car traveling at 7.0 m/s accelerates uniformly at 2.5 m/s2 to reach a speed of 12.0 m/s. How long does this take? With an average acceleration of -1.2 m/s2, how long will it take to bring a bicycle at a speed of 6.5 m/s to a complete stop?

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Problems Continued Turner’s treadmill runs with a velocity of -1.2 m/s and speeds up at regular intervals during a half-hour workout. After 25 min, the velocity is m/s. What is the average acceleration during this period? Suppose a treadmill has an average acceleration of 4.7X10-3 m/s2. How much will the speed change after five minutes? If the initial speed is 1.7m/s, what is the final speed?

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**Displacement With Constant Acceleration**

We will use several equations that include displacement, velocity, acceleration and time. The first is below: ∆𝑥= 1 2 (𝑣𝑖+𝑣𝑓)∆𝑡

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Example A racing car reaches a speed of 42 m/s. It undergoes a constant acceleration and comes to a rest 5.5 s later. How far did the car take to stop?

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Problems A car accelerates uniformly from rest to a speed of 6.6 m/s in 6.5 s. Find the distance. A driver in a car traveling at a speed of 21.8 m/s sees a cat 101 m away on the road. How long will it take for the car to accelerate uniformly to rest in 99 m. A car enters the freeway with a speed of 6.4 m/s and accelerates for 3.2 km in 3.5 min. How fast is the car moving at the end?

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**Velocity and Displacement With Constant Acceleration**

You will use these equations when given the acceleration. 𝑣𝑓=𝑣𝑖+𝑎∆𝑡 ∆𝑥=𝑣𝑖∆𝑡+ 1 2 𝑎 ∆𝑡 2

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Example A plane at rest accelerates at 4.8 m/s2 for 15 seconds and takes off. What is the speed at takeoff? How long must the runway be?

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Problems A car with an initial speed of 6.5 m/s accelerates at a uniform rate of 0.92 m/s2 for 3.6 s. Find the final speed and displacement. An automobile with an initial speed of 4.3 m/s accelerates at 3.0 m/s2. Find the final speed and displacement after 5.0 seconds.

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Problems Continued A car starts from rest and travels for 5.0 s with an acceleration of -1.5 m/s2. What is the final velocity? How far does it travel? A car traveling at 15 m/s applies the brakes and accelerates at -2.0 m/s2. How long does it take to accelerate to 10 m/s? How far did the car travel?

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**Final Velocity After Any Displacement**

This equation can be used when we don’t know the time. 𝑉𝑓2=𝑉𝑖2+2𝑎∆𝑥 Magnitude-

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Example A person pushing a stroller starts from rest and accelerates at 0.5 m/s2. What is the velocity after 4.75 m?

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Problems A car traveling at 7.0 m/s accelerates at 0.8 m/s2 for 245 m. What is the final velocity? What is the velocity after 125 m? A car accelerates from rest at a rate of 2.3 m/s2. What is the speed after 55 m? How long does it take to travel 55 m?

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Problems Continued An aircraft has a liftoff speed of 33 m/s. What minimum acceleration does this require if the plane lifts off after 240 m? A certain car is capable of accelerating at 0.85 m/s2. What is the magnitude of the car’s displacement as it accelerates from 83 km/hr to 94 km/hr?

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Mixed Problems Nathan accelerates his skateboard from rest to 12.5 m/s in 2.5 s. What is his acceleration? What is his displacement? What is his average velocity? Marissa’s car accelerates at a rate of 2.6 m/s2 how long does it take to go from 24.6 m/s to 26.8 m/s?

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Free Fall An object in free fall is falling toward the Earth and the only force acting on it is gravity. Every object experiences the same acceleration due to gravity. g= Also, since the acceleration is downward, g will be negative. The acceleration is the same for an object going straight up.

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Free Fall Example Jason hits a volleyball with an initial velocity of 6.0 m/s upward. If the ball starts 2 m above the floor, how long will it be in the air?

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**Assignment Page 64 1-4 a) -42 m/s b) 11 s a) 22.1 m/s b) 2.25 s**

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