PHSX 114, Monday August 25 Reading for this lecture: Chapter 2 (2-1 thru 2-4)Reading for this lecture: Chapter 2 (2-1 thru 2-4) Reading for the next lecture: Chapter 2 (2-5 thru 2-7)Reading for the next lecture: Chapter 2 (2-5 thru 2-7) Homework for this lecture: Chapter 2, questions: 11, 14; problems: 5, 7, 14.Homework for this lecture: Chapter 2, questions: 11, 14; problems: 5, 7, 14.

Units conversions Multiply by a ratio that is equal to one (ex: 1 hr/60 min) Example (done on presenter).

Your turn: Windsor, Ontario is just across the border from Detroit, Michigan. You are shopping for gasoline in Detroit and find the cost is $1.49/gallon. In Windsor the price is $0.61/L (Canadian). Where is it cheaper to buy gas? (1 USD = CAD) (1 gallon=3.785 L) Answer: The Windsor price converts to $1.63/gallon (U.S.) (0.61*3.785/1.414)

Example of qualitative exam question based on Chapter 1 Which of the following definitions of “theory” best matches the use of the term in science? A. A body of principles governing the study or practice of a discipline B. A broad, detailed, predictive and testable statement about how nature works C. Abstract reasoning D. An assumption E. A guess Answer: B.

Example of quantitative exam question based on Chapter 1, problem 19 A knot is a unit of velocity corresponding to one nautical mile per hour. If a nautical mile is 1852 m, how many meters per second equals one knot? A m/s B. 1.0 m/s C m/s D m/s E x 10 6 m/s Answer: A. (1852/3600)

Kinematics: Chapters 2 and 3 Terminology to describe motionTerminology to describe motion Chapter 2 -- motion in one dimensionChapter 2 -- motion in one dimension Chapter 3 -- motion in more than one dimension (vectors)Chapter 3 -- motion in more than one dimension (vectors) Later chapters discuss the causes of motion ("dynamics")Later chapters discuss the causes of motion ("dynamics")

Where are you? Position (x) One dimensional coordinate axisOne dimensional coordinate axis Positions relative to originPositions relative to origin Positive to right, negative to leftPositive to right, negative to left

Displacement: Δx=x 2 - x 1 Difference between initial and final positionDifference between initial and final position Not distance traveledNot distance traveled ExampleExample

Velocity Average velocity = displacement/time interval = Δx/ΔtAverage velocity = displacement/time interval = Δx/Δt Positive velocity means motion to the right, negative means to the leftPositive velocity means motion to the right, negative means to the left Average speed = distance traveled/time intervalAverage speed = distance traveled/time interval Average speed is always positive (no information about direction)Average speed is always positive (no information about direction) ExampleExample

Your turn: At t=0, your position is x=3 m. At t=2 s, your position is x=7 m. Find a) the displacement, b) the average velocity, c) the average speed Answer: a) 4 m, b) 2 m/s, c) 2 m/s

Instantaneous velocity is the limit of the average velocity as Δt approaches zero How fast am I going right now? (Speedometer reading.)How fast am I going right now? (Speedometer reading.) For those who know calculus: If x(t) gives the position as a function of time, then the instantaneous velocity, v(t), is the derivative of x(t) with respect to t.For those who know calculus: If x(t) gives the position as a function of time, then the instantaneous velocity, v(t), is the derivative of x(t) with respect to t. Instantaneous speed is the magnitude (absolute value) of the instantaneous velocityInstantaneous speed is the magnitude (absolute value) of the instantaneous velocity

Acceleration is the rate of change of the velocity Average acceleration = change in velocity/time interval = Δv/ΔtAverage acceleration = change in velocity/time interval = Δv/Δt Instantaneous acceleration is the limit of the average acceleration as Δt approaches zeroInstantaneous acceleration is the limit of the average acceleration as Δt approaches zero For those who know calculus: If v(t) gives the velocity as a function of time, then the instantaneous acceleration, a(t), is the derivative of v(t) with respect to t.For those who know calculus: If v(t) gives the velocity as a function of time, then the instantaneous acceleration, a(t), is the derivative of v(t) with respect to t. ExamplesExamples

Your Turn: A runner starts from rest and accelerates at a=6 m/s 2. What is her speed after 5 s? Answer: 30 m/s (Δv=v 2 -v 1 =aΔt=(6 m/s 2 )(5s)=30 m/s; v 1 =0, so v 2 =30 m/s.)

What does the sign of the acceleration (positive/negative) signify? Answer: the sign of Δv (not direction of motion)Answer: the sign of Δv (not direction of motion) Example of positive acceleration: v 1 =10 m/s, v 2 =20 m/s, Δt = 5 s, gives a=(20-10)/5 = 2 m/s 2. Note: speeding up with velocity in positive directionExample of positive acceleration: v 1 =10 m/s, v 2 =20 m/s, Δt = 5 s, gives a=(20-10)/5 = 2 m/s 2. Note: speeding up with velocity in positive direction Another example of positive acceleration: v 1 =-20 m/s, v 2 =-10 m/s, Δt = 5 s, gives a=(-10-(-20))/5 = 2 m/s 2. Note: slowing down with velocity in negative directionAnother example of positive acceleration: v 1 =-20 m/s, v 2 =-10 m/s, Δt = 5 s, gives a=(-10-(-20))/5 = 2 m/s 2. Note: slowing down with velocity in negative direction

Your Turn: a) If my acceleration is negative and I'm moving in the positive direction, am I speeding up or slowing down? Answer: a) slowing down (example: v 1 =20 m/s, v 2 =10 m/s, Δt = 5 s, gives a=(10-20)/5 = -2 m/s 2 ) Answer: b) speeding up b) If my acceleration is negative and I'm moving in the negative direction, am I speeding up or slowing down?