Displacement Speed and Velocity Acceleration Equations of Kinematics with Constant A Freely Falling Bodies Graphical Analysis of Velocity and Acceleration

 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= X f -X o  Questions:  Check for understanding pg 29  #1 pg 53

 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 or speed indicates the motion and direction of the motion at each instant in time. V inst = lim x / t as t 0  Check your understanding #6 pg 31

 Acceleration tells us how fast velocity is changing. (m/s/s or m/s 2 )  Average Acceleration is the change in velocity divided by the elapsed time to make that change.  A = v f –v o / t f – t o  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

 For these, unless otherwise noted, X o will be at the origin and T o will be at time = 0 seconds.  There are five kinematic variables:  X = displacement  A = acceleration (constant value)  V = final velocity  V o = initial velocity at T o = 0 seconds.  T = time elapsed since T o = 0 seconds.  Derived equations from the first few are as follows:  V = v o + at  X = vt or v = x/t  V = ½ (v o + v)  X = ½ (v o + v) t  X = v o t + ½ at 2  V 2 = V o 2 + 2ax

 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

 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 V f for one may very well be the V o for the next calculations.  Follow the reasoning rules on pg 43.  Questions #38, 40 pg 55

 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/s 2  Gravity is always a vector acceleration pointing downwards.  #44, #50 pg 55, #59 pg 56