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Chapter Two

Chapter Two. Displacement Speed and Velocity Acceleration Equations of Kinematics with Constant A Freely Falling B odies Graphical Analysis of Velocity and Acceleration. Displacement.

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Chapter Two

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

  2. 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

  3. 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

  4. 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

  5. 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

  6. 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

  7. 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

  8. 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

  9. 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

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