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

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