Acceleration AP Physics C Mrs. Coyle

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

Dt Average Acceleration a = Dv Average Acceleration= Change in Velocity Time a= Vector a = Dv Dt

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

Instantaneous Acceleration a = lim Dv Dt 0 Dt or a = dv dt

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 dt dt dt2

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

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 = lim Dv = lim ( vfinal –vinitial ) Dt 0 Dt Dt 0 Dt vfinal = 3(t +Dt) +1 , vinitial = 3t +1 Ans: a= 3 m/s2 (constant)

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 ,

Uniform Accelerated Motion Motion with constant acceleration Straight line Same direction

Examples of Graphs for Constant Acceleration

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

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

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

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

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