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PHSX 114, Monday August 25

PHSX 114, Monday August 25. Reading for this lecture: Chapter 2 (2-1 thru 2-4) 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. Units conversions Multiply by a ratio that is equal to one (ex: 1 hr/60 min)

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PHSX 114, Monday August 25

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  1. PHSX 114, Monday August 25 • Reading for this lecture: Chapter 2 (2-1 thru 2-4) • 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.

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

  3. 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 = 1.414 CAD) (1 gallon=3.785 L) Answer: The Windsor price converts to $1.63/gallon (U.S.) (0.61*3.785/1.414)

  4. 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.

  5. 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. 0.5144 m/s B. 1.0 m/s C. 1.944 m/s D. 30.87 m/s E. 6.667 x 106 m/s Answer: A. (1852/3600)

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

  7. Where are you? Position (x) • One dimensional coordinate axis • Positions relative to origin • Positive to right, negative to left

  8. Displacement: Δx=x2 - x1 • Difference between initial and final position • Notdistance traveled • Example

  9. Velocity • Average velocity = displacement/time interval = Δx/Δt • Positive velocity means motion to the right, negative means to the left • Average speed = distance traveled/time interval • Average speed is always positive (no information about direction) • Example

  10. 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

  11. Instantaneous velocity is the limit of the average velocity as Δt approaches zero • 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. • Instantaneous speed is the magnitude (absolute value) of the instantaneous velocity

  12. Acceleration is the rate of change of the velocity • Average acceleration = change in velocity/time interval = Δv/Δt • Instantaneous 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. • Examples

  13. Your Turn:A runner starts from rest and accelerates at a=6 m/s2. What is her speed after 5 s? Answer: 30 m/s (Δv=v2-v1=aΔt=(6 m/s2)(5s)=30 m/s; v1=0, so v2=30 m/s.)

  14. What does the sign of the acceleration (positive/negative) signify? • Answer: the sign of Δv (not direction of motion) • Example of positive acceleration: v1=10 m/s, v2=20 m/s, Δt = 5 s, gives a=(20-10)/5 = 2 m/s2. Note: speeding up with velocity in positive direction • Another example of positive acceleration: v1=-20 m/s, v2=-10 m/s, Δt = 5 s, gives a=(-10-(-20))/5 = 2 m/s2. Note: slowing down with velocity in negative direction

  15. 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: v1=20 m/s, v2=10 m/s, Δt = 5 s, gives a=(10-20)/5 = -2 m/s2) b) If my acceleration is negative and I'm moving in the negative direction, am I speeding up or slowing down? Answer: b) speeding up

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