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Today

Learn about position, displacement, velocity, acceleration, and their relationships through examples. Understand how to solve for acceleration and tension in various scenarios.

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Today

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  1. Today • Kinematics: Description of Motion • Position and displacement • Velocity • average • instantaneous • Acceleration • average • instantaneous 09

  2. Example: pulling 2 blocks 30N T 10kg 5kg frictionless • Solve for acceleration • Solve for tension

  3. Clicker Question: pulling 2 blocks 30N T 10kg 5kg friction frictionless • Two blocks are being pulled along by a constant 30N force. Initially the floor is frictionless, but then they encounter a region of friction. When both blocks are over the region where there is friction, what happens to T, the tension between the blocks? • A. T increases • B. T decreases • C. T remains the same

  4. Example: pulling 2 blocks 30N T 10kg 5kg µk= 0.2 • Solve for acceleration • Solve for tension

  5. x (m) 3 t 4 -3 Displacement • Change in position from initial time to final time

  6. v(t) Velocity x(t) • Slope of x vs t gives v vs t • Area under v vs t gives Dx! • Which plot best represents v(t) 4s Dx Dt t 5s v(t) v(t) t t t

  7. v(t) v(t) Dv t Dt Acceleration (m/s2) • The average acceleration is the change in velocity divided by the change in time. • Instantaneous acceleration is limit of average velocity as Dt gets small. It is the slope of the v(t) plot t 31

  8. x (m) 3 t 4 -3 Position vs Time Plots • Gives location at any time. • Displacement is change in position. • Slope gives velocity. Position at t=3, x(3) = Displacement between t=1 and t=5.Dx = Average velocity between t=1 and t=5. v = 12

  9. velocity at t=2, v(2) = Displacement between t=0 and t=3: Dx= Average velocity between t=0 and t=3? v= Change in v between t=3 and t=5. Dv = Average acceleration between t=3 and t=5: a = Velocity vs Time Plots v (m/s) • Gives velocity at any time. • Area gives displacement • Slope gives acceleration. 3 1.5 6 t 4 -3 18

  10. Acceleration at t=4, a(4) = Change in v between t=1 and t=4. Dv = Acceleration vs Time Plots • Gives acceleration at any time. • Area gives change in velocity a (m/s2) 3 t 4 t=1-3: Dv = -3 t=3-4: Dv = 21

  11. Graphs

  12. Graphs

  13. Direction, Direction, Direction Velocity Acceleration Type of motion + + + - - - - +

  14. v v v A B 3 3 3 C t t t 4 4 4 -2 -2 -2 v v 3 3 E D y t x t 4 4 -2 -2 Clicker Question: Dropped Ball • A ball is dropped from a height of two meters above the ground. • Draw vy vs t 34

  15. v v v A B C 3 3 3 t t t 4 4 4 -2 -2 -2 v v 3 3 D E y t x t 4 4 -2 -2 Clicker Question: Tossed Ball • A ball is tossed from the ground up a height of two meters above the ground. And falls back down • Draw v vs t 42

  16. position vs. time Example: position vs. time • Where is velocity zero? • Where is velocity positive? • Where is velocity negative? • Where is speed largest? • Where is acceleration zero? • Where is acceleration positive? 48

  17. velocity vs. time Example: velocity vs. time • Where is velocity zero? • Where is velocity positive? • Where is velocity negative? • Where is speed largest? • Where is acceleration zero? • Where is acceleration positive?

  18. Summary of Concepts • kinematics: A description of motion • position:your coordinates • displacement:x = change of position • velocity:rate of change of position • average : x/t • instantaneous: slope of x vs. t • acceleration:rate of change of velocity • average: v/t • instantaneous: slope of v vs. t 50

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