Acceleration
AP Physics CMrs. Coyle
Average Acceleration Instantaneous Acceleration Negative Acceleration Deceleration Graphical Analysis Using the limit to find acceleration
Average Acceleration
Average Acceleration= Change in Velocity
Time
a=
Vector
a = vt
Instantaneous Acceleration
Instantaneous Acceleration Acceleration at a given instant
Can you tell if you are accelerating if you observe the speedometer of a car?
Instantaneous Acceleration
or
a = lim vt 0t
a = dvdt
Acceleration is the derivative of v with respect to time.a = dvdt
a = d ( dx ) = d2 x
dt dt dt2
Acceleration is the second derivative of x with respect to time.
Negative Acceleration: acceleration in the negative direction (can lead to either increasing v or decreasing v).
Deceleration: acceleration leading to 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 v = lim ( vfinal –vinitial )
t 0t t
0t
vfinal = 3(tt) +1 , vinitial = 3t +1
Ans: a= 3 m/s2 (constant)
The velocity of a toy rocket is given by
v= 4t2 + 3 (t is in sec).
a) Find the expression for instantaneous acceleration at any instant. (using the limit).
b) Find the instantaneous acceleration at t= 2s.
c) Find the average acceleration from 0 to 2sec.
Answer: a)8t, b) 16 m/s2 ,c) 8m/s2 ,
Example 2
Uniform Accelerated Motion
Motion with constant acceleration Straight line Same direction
Examples of Graphs for Constant Acceleration
Example of Position vs Time (constant a)
Time (s)
o
Position (m)
Parabola
Slope of Tangent at a given time= Instantaneous Velocity at that time
Example of Velocity vs Time (Constant Acceleration)
Time (s)o
Velocity (m/s)
Slope of Line= Acceleration
Area Under Line=Displacement
Example of Acceleration vs Time (Const. a)
Time (s)
o
Acceleration (m/s2)
Area under line = Change in Velocity
Example:(see handout“Graphical Kinematic Exercises II”)
Example:(see handout)
What motion could these represent? 0
0
0