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.

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.

Scalar Vs. Vector Scalar Vector

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:

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:

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?

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?

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?

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-

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

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:

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

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?

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?

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 -6.5 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?

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

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?

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?

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

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?

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.

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?

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

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

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?

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?

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?

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.

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?

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