1. Acceleration
AP Physics C Mrs. Coyle

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

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

4. 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 = lim Dv
Dt  Dt 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
dt dt 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 (t is in sec).
Find an expression that gives the instantaneous acceleration at any time t.
Strategy: a = lim Dv = lim ( vfinal –vinitial )
Dt  Dt Dt  Dt
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= 4t (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?