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PHYSICS 231 Lecture 2: Motion in 1 dimension, part I

PHYSICS 231 Lecture 2: Motion in 1 dimension, part I. Remco Zegers Walk-in hour: Thursday 11:30-13:30 Helproom. Galileo (1564-1642). What mathematical forces govern accelerated motion?. A wooden and stone sphere are dropped from the tower of pisa. Which one reaches the earth first?.

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PHYSICS 231 Lecture 2: Motion in 1 dimension, part I

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  1. PHYSICS 231Lecture 2: Motion in 1 dimension, part I Remco Zegers Walk-in hour: Thursday 11:30-13:30 Helproom PHY 231

  2. Galileo (1564-1642) What mathematical forces govern accelerated motion? A wooden and stone sphere are dropped from the tower of pisa. Which one reaches the earth first? Answer: same time! PHY 231

  3. The inclined plane experiment Distance traveled goes with the square of time: x(t)~t2 Time measured with water! PHY 231

  4. X=30 t=1 t=0 X=0 X=30 X=45 X=-30 t=0 t=1 X=0 X=30 X=45 Displacement Displacement is a vector and thus has direction (sign) Displacement is not equal to Distance PHY 231

  5. t=2 t=0 t=1 t=0 t=1 t=2 X=0 X=30 X=45 Which object has the largest average velocity over 2 s? Same! Average Velocity Displacement Average velocity= Time interval PHY 231

  6. Graphically x(m) = slope t(s) The average velocity is the slope of the line connecting begin end end point in the x-t graph. Ignore what happens in between. PHY 231

  7. X=-30 t=0 t=1 X=0 X=30 X=45 Vectors and Scalars... =-30 Average velocity:vector =+30 Average speed:scalar PHY 231

  8. Instantaneous Velocity “But officer, my average speed was only 25 miles per hour...” Sometimes we want to know the speed at one particular point in time. PHY 231

  9. Instantaneous velocity x(m) t(s) What is the Velocity at t=2.0 s? Consider the average velocity for a very small time interval with t=2.0 s in the center! PHY 231

  10. Instantaneous velocity x(m) x t t(s) PHY 231

  11. Instantaneous velocity x(m) x t t(s) v=slope of the tangent to the x-t curve at t=2.0 s Think about the sign! PHY 231

  12. B B Question x A B t Which object had the largest average velocity? Which object had the largest instantaneous velocity? PHY 231

  13. v …means a change in velocity: Acceleration t Acceleration x A change in slope in the x-t graph… t PHY 231

  14. Instantaneous acceleration: Acceleration Average acceleration PHY 231

  15. Question v t=0,v=20 t=1, v=5 t What is the average acceleration between t=0 and t=1 A) 15 B) -15 C) 0 D) infinity PHY 231

  16. Question GALILEO! Which v-t diagram matches which a-t diagram? PHY 231

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