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Acceleration

Acceleration . AP Physics C Mrs. Coyle . Average Acceleration Instantaneous Acceleration Negative Acceleration Deceleration Graphical Analysis Using the limit to find acceleration. Average Acceleration. Average Acceleration= Change in Velocity Time

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Acceleration

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  1. Acceleration AP Physics CMrs. Coyle

  2. Average Acceleration • Instantaneous Acceleration • Negative Acceleration • Deceleration • Graphical Analysis • Using the limit to find acceleration

  3. Average Acceleration • Average Acceleration= Change in Velocity Time a= • Vector a = Dv Dt

  4. Instantaneous Acceleration • Instantaneous Acceleration • Acceleration at a given instant • Can you tell if you are accelerating if you observe the speedometer of a car?

  5. Instantaneous Acceleration a = limDv Dt0Dt or a = dv dt

  6. Acceleration is the derivative of v with respect to time. a = dv dt Acceleration is the second derivative of x with respect to time. a = d ( dx ) = d2 x dtdt dt2

  7. Deceleration: acceleration leading to decreasing v. • Negative Acceleration: acceleration in the negative direction (can lead to either increasing v or decreasing v).

  8. Example 1: Using the limit to find instantaneous acceleration from a velocity function. The velocity of a particle is given by v= 3t + 1 (t is in sec). Find an expression that gives the instantaneous acceleration at any time t. Strategy: a = limDv = lim (vfinal –vinitial ) Dt0DtDt0Dt vfinal = 3(t +Dt) +1 , vinitial = 3t +1 Ans: a= 3 m/s2 (constant)

  9. Example 2 The velocity of a toy rocket is given by v= 4t2 + 3 (t is in sec). • Find the expression for instantaneous acceleration at any instant. (using the limit). • Find the instantaneous acceleration at t= 2s. • Find the average acceleration from 0 to 2sec. Answer: a)8t, b) 16 m/s2 ,c) 8m/s2 ,

  10. Uniform Accelerated Motion • Motion with constant acceleration • Straight line • Same direction

  11. Examples of Graphs for Constant Acceleration

  12. Example of Position vs Time (constant a) Parabola Position (m) o Time (s) Slope of Tangent at a given time= Instantaneous Velocity at that time

  13. Example of Velocity vs Time (Constant Acceleration) Velocity (m/s) o Time (s) Slope of Line= Acceleration Area Under Line=Displacement

  14. Example of Acceleration vs Time (Const. a) Acceleration (m/s2) o Time (s) Area under line = Change in Velocity

  15. Example:(see handout“Graphical Kinematic Exercises II”)

  16. Example:(see handout)What motion could these represent? 0 0 0

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