Linear Kinematics Chapter 2 in the text 11232020

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Linear Kinematics Chapter 2 in the text 11/23/2020 Dr. Sasho Mac. Kenzie - HK

Linear Kinematics Chapter 2 in the text 11/23/2020 Dr. Sasho Mac. Kenzie - HK 376 1

KINEMATICS LINEAR Next Class ANGULAR Vectors Scalars Distance Displacement Velocity Speed Acceleration 11/23/2020 Dr.

KINEMATICS LINEAR Next Class ANGULAR Vectors Scalars Distance Displacement Velocity Speed Acceleration 11/23/2020 Dr. Sasho Mac. Kenzie - HK 376 2

Scalars • A measure that only considers magnitude • Does not consider direction •

Scalars • A measure that only considers magnitude • Does not consider direction • E. g. , a distance of 15 meters is a scalar measure 15 m • The line is 15 meters but has no direction 11/23/2020 Dr. Sasho Mac. Kenzie - HK 376 3

Vectors • Describes both a magnitude and direction • E. g. , a displacement

Vectors • Describes both a magnitude and direction • E. g. , a displacement of 15 meters in the positive direction is a vector. • Represented by arrows, in which the length represents magnitude and orientation represents direction. + 15 m • The arrow is 15 meters in the positive direction 11/23/2020 Dr. Sasho Mac. Kenzie - HK 376 4

Distance • A measure of the length of the path followed by an object

Distance • A measure of the length of the path followed by an object from its initial to final position. • A scalar quantity (no direction) 11/23/2020 Dr. Sasho Mac. Kenzie - HK 376 5

Speed • The rate of motion of an object • The rate at which

Speed • The rate of motion of an object • The rate at which an object’s position is changing. • A scalar quantity (no direction) 11/23/2020 Dr. Sasho Mac. Kenzie - HK 376 6

Displacement • The straight-line distance in a specific direction from the starting position to

Displacement • The straight-line distance in a specific direction from the starting position to the ending position. • A vector quantity (must have direction) • As the crow flies 11/23/2020 Dr. Sasho Mac. Kenzie - HK 376 7

Velocity • The rate of motion in a specific direction • Same as speed

Velocity • The rate of motion in a specific direction • Same as speed but with a direction • A vector quantity 11/23/2020 Dr. Sasho Mac. Kenzie - HK 376 8

N W Distance vs. Displacement E S 10 km End 5 km Start Distance

N W Distance vs. Displacement E S 10 km End 5 km Start Distance Displacement 11/23/2020 Dr. Sasho Mac. Kenzie - HK 376 9

Speed vs. Velocity It took Billy 3. 5 hours in total to walk 5

Speed vs. Velocity It took Billy 3. 5 hours in total to walk 5 km North and 10 km East. What was Billy’s average speed and average velocity? Speed 11/23/2020 Velocity Dr. Sasho Mac. Kenzie - HK 376 10

Acceleration • The rate at which an object’s speed or velocity changes. • When

Acceleration • The rate at which an object’s speed or velocity changes. • When an object speeds up, slows down, starts, stops, or changes direction, it is accelerating. • Always a vector quantity (has direction) 11/23/2020 Dr. Sasho Mac. Kenzie - HK 376 11

Acceleration • The direction of motion does not indicate the direction of acceleration. •

Acceleration • The direction of motion does not indicate the direction of acceleration. • An object can be accelerating even if its speed remains unchanged. The acceleration could be due to a change in direction not magnitude. 11/23/2020 Dr. Sasho Mac. Kenzie - HK 376 12

Midterm Example Bolt runs 200 m in 19. 19 seconds. Assume he ran on

Midterm Example Bolt runs 200 m in 19. 19 seconds. Assume he ran on the inside line of lane 1, which makes a semicircle (r = 36. 5 m) for the first part of the race. He runs the curve in 11 s. Circle Circumference = 2 r; Circle Diameter = 2 r; r is radius Start N 36. 5 m W E S 1. 2. 3. 4. 5. 6. 7. 8. What distance was run on the curve? What was his displacement after the curve? Total distance? Total displacement? Average velocity on the curve? Average speed on the curve? Average velocity for the race? Average speed for the race? Finish 11/23/2020 Dr. Sasho Mac. Kenzie - HK 376 13

Midterm Example Bolt runs 200 m in 19. 19 seconds. Assume he ran on

Midterm Example Bolt runs 200 m in 19. 19 seconds. Assume he ran on the inside line of lane 1, which makes a semicircle (r = 36. 5 m) for the first part of the race. He runs the curve in 11 s. Circle Circumference = 2 r; Circle Diameter = 2 r; r is radius Start N 36. 5 m W E S 1. 2. 3. 4. 5. 6. 7. 8. What distance was run on the curve? What was his displacement after the curve? Total distance? Total displacement? Average velocity on the curve? Average speed on the curve? Average velocity for the race? Average speed for the race? Finish 11/23/2020 Dr. Sasho Mac. Kenzie - HK 376 14

Instantaneous Velocity • The average velocity over an infinitely small time period. • Determined

Instantaneous Velocity • The average velocity over an infinitely small time period. • Determined using Calculus • The derivative of displacement • The slope of the displacement curve 11/23/2020 Dr. Sasho Mac. Kenzie - HK 376 15

Instantaneous Acceleration • The average acceleration over an infinitely small time period. • Determined

Instantaneous Acceleration • The average acceleration over an infinitely small time period. • Determined using Calculus • The derivative of velocity • The slope of the velocity curve 11/23/2020 Dr. Sasho Mac. Kenzie - HK 376 16

Slope Y (4, 8) 8 (0, 0) 4 X Slope = rise = Y

Slope Y (4, 8) 8 (0, 0) 4 X Slope = rise = Y 2 – Y 1 = 8 – 0 = 8 = 2 run X X 2 – X 1 4– 0 4 11/23/2020 Dr. Sasho Mac. Kenzie - HK 376 17

Velocity is the slope of Displacement Y (4, 8) 8 Displacement (m) (0, 0)

Velocity is the slope of Displacement Y (4, 8) 8 Displacement (m) (0, 0) Time (s) 4 X Average Velocity = rise = D 2 – D 1 = 8 – 0 = 8 m = 2 m/s run t t 2 – t 1 4– 0 4 s 11/23/2020 Dr. Sasho Mac. Kenzie - HK 376 18

1. The displacement graph on the previous slide was a straight line, therefore it’s

1. The displacement graph on the previous slide was a straight line, therefore it’s slope was 2 at every instant. 2. Which means the velocity at any instant is equal to the average velocity. 3. However if the graph was not straight the instantaneous velocity could not be determined from the average velocity. 11/23/2020 Dr. Sasho Mac. Kenzie - HK 376 19

Average vs. Instantaneous Y The average velocity does not accurately represent slope at this

Average vs. Instantaneous Y The average velocity does not accurately represent slope at this particular point. 8 (4, 8) Displacement (m) (0, 0) Time (s) 4 X Average Velocity = rise = D 2 – D 1 = 8 – 0 = 8 m = 2 m/s run t t 2 – t 1 4– 0 4 s • Read Ch. 6 pages 147 -158 for next class 11/23/2020 Dr. Sasho Mac. Kenzie - HK 376 20