CHAPTER TWO

DisplacementSpeed and Velocity

AccelerationEquations of Kinematics with Constant A

Freely Falling BodiesGraphical Analysis of Velocity and

Acceleration

Displacement

The displacement is a vector that points from an object’s initial position to its final position and has a magnitude that equals the shortest distance between the two positions. (meters)

X= Xf -Xo Questions:

Check for understanding pg 29 #1 pg 53

Speed and Velocity Average speed is the distance traveled divided

by the time required to cover the distance. Avg speed = Distance/Elapsed time

Average velocity is the displacement of the car divided by the time required to cover the distance. Avg velocity (V) = X / t

For velocity, you must take the direction into account. If the displacement is in the positive direction, the velocity will be positive.

Questions: Example 2 #8, #10 page 53

Speed and velocity will be designated with V

Instantaneous Velocity

Instantaneous Velocity or speed indicates the motion and direction of the motion at each instant in time.

Vinst = lim x / t as t 0

Check your understanding #6 pg 31

Acceleration Acceleration tells us how fast velocity is

changing. (m/s/s or m/s2) Average Acceleration is the change in velocity

divided by the elapsed time to make that change. A = vf –vo / tf – to

Instantaneous acceleration is limit as change in time approaches zero.

Questions: Example #3 pg 33 (units) Whenever the acceleration and the velocity

vectors have opposite directions, the object is slowing down, or ‘decelerating’.

Questions: #18, 19 pg 54

Equations for Constant Acceleration Situations

For these, unless otherwise noted, Xo will be at the origin and To will be at time = 0 seconds.

There are five kinematic variables: X = displacement A = acceleration (constant value) V = final velocity Vo = initial velocity at To = 0 seconds. T = time elapsed since To = 0 seconds.

Derived equations from the first few are as follows: V = vo + at X = vt or v = x/t V = ½ (vo + v) X = ½ (vo + v) t X = vot + ½ at2

V2 = Vo2 + 2ax

Solving Equations for Constant Acceleration Problems

These equations assume that the acceleration of an object is uniform over the time interval in question. AP Physics B exam generally deals with uniform acceleration so this list of equations is very helpful!

Example 5 pg 36 *Decide at the start which direction will be

positive and which is negative relative to the coordinate system

*As you reason through the problem, be sure to interpret the term decelerating.

Questions: # 24, #26 pg 54

Problem solving!!

The motion of two objects may be interrelated so that they share a common variable.

Often when the motion of an object is divided into two segments, each will have its own acceleration. When solving such problems it is important to realize that the Vf for one may very well be the Vo for the next calculations.

Follow the reasoning rules on pg 43. Questions #38, 40 pg 55

Freely Falling Bodies

Effect of gravity on all things making them fall towards the earth is an idealized motion we call free fall.

Since the acceleration is constant for free fall, the kinematic equations can be used with the acceleration due to gravity (g) = 9.80 m/s2

Gravity is always a vector acceleration pointing downwards.

#44, #50 pg 55, #59 pg 56