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Announcements

Announcements. No class next Monday (MLK day) Do MasteringPhysics homework Homework 00 open ‘til Friday 10 PM Homework 01 will open soon Written Homework due next Friday Book problems 2.37 and 2.71. Describing Motion. acceleration. §2.3–2.4. Board Work.

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Announcements

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  1. Announcements • No class nextMonday (MLK day) • Do MasteringPhysics homework • Homework 00 open ‘til Friday 10 PM • Homework 01 will open soon • Written Homework due next Friday • Book problems 2.37 and 2.71

  2. Describing Motion acceleration §2.3–2.4

  3. Board Work A car waits at a stop light for 5 seconds, smoothly accelerates to 15 m/s over 5 seconds, and then continues at 15 m/s. Describe the car’s motion using a velocity-time graph.

  4. Dv average acceleration = Dt over the entire interval Dv instantaneous acceleration = lim Dt Dt 0 at one instant Acceleration Rate of changing velocity = dv/dt = d2x/dt2

  5. Poll Question What is the SIunit for acceleration? • m. • s. • m·s. • m/s. • m2/s. • m/s2. • m2/s2.

  6. Visualize Acceleration Young and Freedman, Fig. 2.8 Board Work: • Signs of v • Signs of a

  7. Group Work In earlier car scenario: • What is the car’s acceleration during the different segments of its motion? • Describe the car’s motion using an acceleration-time graph.

  8. Equations of Motion as functions of time

  9. Find Position from Velocity • Generally: velocity is derivative of position wrt time dx/dt. • Conversely, position is the integral of velocity over time. v = dx/dt dx = vdt ∫dx = ∫vdt x=∫vdt + x0 What is this when v is constant?

  10. distance units Integral of v-t graph area = (a m/s)(b s) = ab m speed (m/s) a b time (s)

  11. Constant Acceleration • Instantaneous accel = average accel • a = Dv/Dt • Dv = velocity change over time Dt • Dv = aDt • v = v0 + Dv = v0 + aDt

  12. Find Velocity from Acceleration • General case: acceleration is derivative of velocity wrt time dv/dt. • Conversely, velocity is the integral of acceleration over time. a = dv/dt dv = adt ∫dv = ∫adt v=∫adt + v0 What is this when a is constant?

  13. Equations of Motion • What are velocity and position under conditions of constant acceleration?

  14. Formulas from Constant x-Acceleration • Velocity change Dv = aDt • Velocity vt = v0 + Dv = v0 + aDt • Position change Dx = v0Dt + 1/2 a (Dt)2 • Position xt = x0 + v0Dt + 1/2 a (Dt)2

  15. Another Form (constant a) • If you don’t know Dt and want v: x = x0 + v0Dt + 1/2a (Dt)2Dt = Dv/a x – x0 = v0 Dv/a + 1/2a (Dv/a)2 2a (x–x0) = 2v0 (v–v0) + (v–v0)2 2a (x–x0) = 2vv0 – 2v02 + v2 – 2vv0 + v02 2a (x–x0) = 2vv0 – 2vv0 + v2 + v02 – 2v02 2a (x–x0) = v2 – v02 v2 = v02 + 2a (x–x0) Do units check out?

  16. Another Form (constant a) • If you don’t know a but know v, v0, and Dt: x = x0 + v0Dt + 1/2a (Dt)2a = Dv/Dt = (v–v0)/Dt x = x0 + v0 Dt + 1/2((v–v0)/Dt) (Dt)2 x – x0 = v0 Dt + 1/2v Dt – 1/2v0 Dt x – x0 = v0 Dt – 1/2v0 Dt + 1/2v Dt x – x0 = 1/2 (v0 + v)Dt Do units check out?

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