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**Period 1**• Pg. 29-31 • Ques: 27, 33, 36, 56, 58a, 60-62, 66, 68b**Warm-Up Questions**• Just think, what is the difference between… • Speed & Velocity? • Distance & Displacement**Motion…(in a straight line)**• An object is in motion if… …it changes position …or… travels a distance • How do we typically describe motion? • Speed • Units…?? • Distance & Time -- Equation??**Speed vs. Velocity**• What’s the difference? • Speed = • Velocity = • Difference btwn. Distance & displacement then? • Dist = total path length an object covered during its motion • Disp = directional distance between an object’s starting and ending points of motion -- Velocity Equation???**Scalar vs. Vector Quantities**• Scalar • Quantities that are described by magnitude alone • Vector • Quantities that are described by BOTH a magnitude and direction**Examples: Scalar or Vector??**• Distance = _______ • Displacement = _______ • Time = _______ • Mass = _______ • Velocity = _______ • Speed = _______ • Acceleration = _______**Vector Addition**• A vector is represented by an arrow • Drawn to scale and points in the direction of the motion • NET outcome = resultant vector ***Sum all the vectors in x direction & sum all vectors in y direction, then find magnitude of resultant vector • Example: • A car drives 5 km east, stops, and drives another 3 km east. Draw the 2 initial vectors and the resultant vector.**Vector Addition**• A vector is represented by an arrow • Drawn to scale and points in the direction of the motion • NET outcome = resultant vector • Example: • A car drives 2 km east, stops, drives 10 km west, stops, and then drives another 3 km east again. Draw the 3 initial vectors and the resultant vector.*****Need to Know Equations*****• Avg. Speed = • Avg. Velocity = • Final Position =**Question…**• A hiker walks 6 km west and then turns abruptly and immediately walks another 8 km north and stops to catch his breath. • What was the distance that he hiked so far? • What was the displacement of his hike so far?**Use Trig to find Direction**• A hiker walks 6 km west and then turns abruptly and immediately walks another 8 km north and stops to catch his breath. • What was the displacement of his hike so far?****Circumference = 2 r ****Question • A BPHS track star runs the 100 m turn (half circle portion at the end of the track) in 16 s. • What distance did they run? Displacement? • What was their speed? Velocity?**Warm-Up Question**• A jogger jogs 300 m straight in one direction in 2.5 min and then jogs back to the starting point in 3.3 min. What was the jogger’s avg velocity: • On the way down? • On the way back to the starting point? • For the total jog?**Instantaneous Velocity**• Defined as: • How fast something is moving in which direction at a particular instant of time • When dealing with uniform motion, how are inst. velocity and avg. velocity related?**Nonuniform Motion**• How would you find the inst. velocity of an object’s motion that looked like: Position Time**Nonuniform Motion**• How would you find the inst. velocity of an object’s motion that looked like:**Nonuniform Motion**• How would you find the inst. velocity of an object’s motion that looked like:**Math Problems**• Book: • Pg. 60-61 -> 1, 7, 8, 10, 13-14, 16, 21, (22 = Bonus)**Acceleration**• Defined as: • Rate at which velocity changes • Velocity changes when: • An object speeds up or slows down • An object changes its direction of motion • So when does an object accelerate?*****Need to Know Equations*****• Avg. Acceleration = • Final Velocity (w/ constant acceleration) =**Acceleration Math**• A car has an initial velocity of 80 m/s. It slows down to a stop in 8 seconds. What was the cars acceleration during this time?**Average Velocity Question…**• What was the average velocity of that car as it constantly accelerated during that time period?*****Need to Know Equations*****• Avg. Acceleration = • Final Velocity (w/ constant acceleration) = • Avg. Velocity (w/ constant acceleration) =**Math Problems**• Pg. 61-62 23-27, 30, 32-34**Kinematic Equations**• Some physics problems are hard to do because they require the application of multiple equations throughout one question. • How can we make our lives easier…? • Let’s combine a couple of our equations algebraically in advance**Deriving Equations**• Final position w/o avg. velocity & acceleration: • Xfeq: • Avg. V eq: • Combined (sub in for avg. v):**Deriving Equations**• Final position w/o avg. velocity & acceleration: xf = xi + ½(vf + vi)t**Deriving Equations**• Displacement when object accelerates w/o vf:**Deriving Equations**• Displacement when object accelerates w/o vf: • Use previous equation: • Vfeq: • Combined (sub in for Vf):**Deriving Equations**• Displacement when object accelerates w/o vf: xf = xi + vit + ½at2**Deriving Equations**• Displacement when object accelerates from rest: xf = xi + vit + ½at2 xf = xi + ½at2 xf = ½at2**Deriving Equations**• Displacement, Velocity, & Acceleration w/o Time: • Use Vfeq: • xf = xi + ½(vf + vi)t eq:**Deriving Equations**• Displacement, Velocity, & Acceleration w/o Time:**Deriving Equations**• Displacement, Velocity, & Acceleration w/o Time: vf2= vi2 + 2a(xf – xi)**Example Math Problem**A rocket is shot horizontally from a soldier’s rocket launcher with a constant acceleration of 20m/s2. After 10 seconds, how fast is the rocket moving & how far has it traveled?**Example Math Problem**A rocket is shot horizontally from a soldier’s rocket launcher with a constant acceleration of 20m/s2. After 10 seconds, how fast is the rocket moving & how far has it traveled?**Math Problems**• Pg. 62 38 - 42**Additional Lab Questions**• What should the slope of the line for the graph that you drew be equal to? (Name & Value…think about rise over run) • Knowing this, what equation can we then derive to solve for the acceleration of an object on an inclined plane? • What was the percent error between the extrapolated value and the accepted value of g?**Free Fall**• Defined as: • When an object in motion is influenced only by the pull of gravity • Value of Gravity = - 9.8 m/s2**Gravity**• Does the acceleration of an object due to gravity ever change? • Acceleration due to g is constant! • Constant acceleration = which equations??? • Can it be different in different regions on Earth? • YES! Due to…. • Distance from Earth’s center • Air resistance**Math Problems**• Pg. 63-64 59-62, 64-67, 70a