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Acceleration and Instantaneous Velocity

Acceleration and Instantaneous Velocity. You drive the path, and your odometer goes up by 8 miles (your distance). Your displacement is the shorter directed distance from start to stop (yellow arrow). What if you drove in a circle?. Distance vs. Displacement. start. stop. Speed.

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Acceleration and Instantaneous Velocity

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  1. Acceleration and Instantaneous Velocity

  2. You drive the path, and your odometer goes up by 8 miles (your distance). Your displacement is the shorter directed distance from start to stop (yellow arrow). What if you drove in a circle? Distance vs. Displacement start stop

  3. Speed • Velocity is displacement (with equations using the same symbols!) • Speed is distance / time or more accurately

  4. Average Speed • Two ways to look at it

  5. Acceleration • Acceleration is • Acceleration is a VECTOR quantity • Units: Units of v is m/sec;units of t is sec • Units of a is m/sec2

  6. What is the velocity at each point? What is the average velocity?

  7. What is velocity? What is Instantaneous velocity? is made very small – infinitesimally small

  8. What is happening to the velocity in this diagram?

  9. Finding instantaneous velocity • Find the slope using small values of t and d. • Find the tangent to the line of d vs t.

  10. Instantaneous velocity V3 V2 V1

  11. Acceleration is a change in velocity over time. V3 V2 V1

  12. Is there a meaning to the area under the line?

  13. d = v t The area under the curve is given by v * t. The area under the curve is the distance.

  14. Questions • What if acceleration is in the same direction as velocity? • What if acceleration is in the opposite direction from velocity?

  15. Equations •  v = (df - di)/t • vt = (df - di )  df = di + vt (d = vt) • (vf – vi)/t = a • (vf – vi) = at  vf = vi + at • We usually ignore Dt = (tf – ti) and just use t since we can arbitrarily start the clock when we declare t=0

  16. Examples Asher is driving at 10m/sec (22 miles/hour) and accelerates at a rate of 1m/sec/sec (1m/sec2) for a period of 10 seconds. What is Asher’s final velocity? Sarah jumps out of an airplane. Her initial vertical velocity was 0 m/sec. Gravity accelerates a falling body at a rate of 9.8m/sec2 near the surface of the Earth. What is Sarah’s velocity after 5 seconds of free fall? What is this in mph? If Sarah keeps falling for another 5 seconds, will her velocity double? (Hint: Sarah is falling “spread-eagled”)

  17. SAWITESU Show All Work Including The EquationS and Units

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