7/2/2015Dr. Sasho MacKenzie - HK 3761 Linear Kinematics Chapter 2 in the text

7/2/2015Dr. Sasho MacKenzie - HK 3762 KINEMATICS LINEARANGULAR ScalarsDistanceSpeed VectorsDisplacementVelocityAcceleration Next Class

7/2/2015Dr. Sasho MacKenzie - HK 3763 Scalars A measure that only considers magnitude Does not consider direction E.g., a distance of 15 meters is a scalar measure The line is 15 meters but has no direction The line is 15 meters but has no direction 15 m

7/2/2015Dr. Sasho MacKenzie - HK 3764 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 m The arrow is 15 meters in the positive direction The arrow is 15 meters in the positive direction

7/2/2015Dr. Sasho MacKenzie - HK 3765 Distance A measure of the length of the path followed by an object from its initial to final position. A scalar quantity (no direction)

7/2/2015Dr. Sasho MacKenzie - HK 3766 Speed The rate of motion of an object The rate at which an object’s position is changing. A scalar quantity (no direction)

7/2/2015Dr. Sasho MacKenzie - HK 3767 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

7/2/2015Dr. Sasho MacKenzie - HK 3768 Velocity The rate of motion in a specific direction Same as speed but with a direction A vector quantity

7/2/2015Dr. Sasho MacKenzie - HK 3769 Distance vs. DisplacementNWE S Start 5 km End 10 km Distance Displacement

7/2/2015Dr. Sasho MacKenzie - HK 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? SpeedVelocity

7/2/2015Dr. Sasho MacKenzie - HK 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)

7/2/2015Dr. Sasho MacKenzie - HK 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.

Midterm Example 7/2/2015Dr. Sasho MacKenzie - HK Bolt runs 200 m in 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 m 1.What distance was run on the curve? 2.What was his displacement after the curve? 3.Total distance? 4.Total displacement? 5.Average velocity on the curve? 6.Average speed on the curve? 7.Average velocity for the race? 8.Average speed for the race?NWE S Start Finish Circle Circumference = 2  r; Circle Diameter = 2r; r is radius

Midterm Example 7/2/2015Dr. Sasho MacKenzie - HK Bolt runs 200 m in 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 m 1.What distance was run on the curve? 2.What was his displacement after the curve? 3.Total distance? 4.Total displacement? 5.Average velocity on the curve? 6.Average speed on the curve? 7.Average velocity for the race? 8.Average speed for the race?NWE S Start Finish Circle Circumference = 2  r; Circle Diameter = 2r; r is radius

7/2/2015Dr. Sasho MacKenzie - HK Instantaneous Velocity The average velocity over an infinitely small time period. Determined using Calculus The derivative of displacement The slope of the displacement curve

7/2/2015Dr. Sasho MacKenzie - HK Instantaneous Acceleration The average acceleration over an infinitely small time period. Determined using Calculus The derivative of velocity The slope of the velocity curve

7/2/2015Dr. Sasho MacKenzie - HK Slope X Y (0,0) (4,8) 8 4 Slope = rise =  Y = Y2 – Y1 = 8 – 0 = 8 = 2 run  X X2 – X1 4 – 0 4 run  X X2 – X1 4 – 0 4

7/2/2015Dr. Sasho MacKenzie - HK Velocity is the slope of DisplacementX Y (0,0) (4,8) 8 4 Average Velocity = rise =  D = D2 – D1 = 8 – 0 = 8 m = 2 m/s run  t t2 – t1 4 – 0 4 s run  t t2 – t1 4 – 0 4 s Displacement(m) Time (s)

7/2/2015Dr. Sasho MacKenzie - HK 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.

7/2/2015Dr. Sasho MacKenzie - HK Average vs. InstantaneousAverage Velocity = rise =  D = D2 – D1 = 8 – 0 = 8 m = 2 m/s run  t t2 – t1 4 – 0 4 s run  t t2 – t1 4 – 0 4 s XY8 4 Displacement(m) Time (s) (0,0)(4,8) The average velocity does not accurately represent slope at this particular point. Read Ch. 6 pages for next class