 # Physics 521 Section 2.4 and Chapter 3.  Acceleration is the rate at which the velocity of an object changes.  When the velocity changes ( ) during some.

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Physics 521 Section 2.4 and Chapter 3

 Acceleration is the rate at which the velocity of an object changes.  When the velocity changes ( ) during some time interval ( Δt ), the average acceleration can be found using:  The units for acceleration are m/s 2, that tells how many meters per second the velocity changes every second.

 Acceleration is a vector (size and direction).  In straight line motion, acceleration can be positive or negative.  Ex. When a car is speeding up (velocity is increasing), the is a positive number and therefore so is the acceleration.  Ex. When a car is slowing down (velocity is decreasing), the is a negative number and therefore, so is the acceleration.

 An object can have a negative acceleration without slowing down. ◦ Ex. The object can be traveling backwards or towards a more negative position.  An object can have a positive acceleration even though it is slowing down. ◦ Ex. The object is slowing down as it is traveling in a negative direction.

 VT graphs describe motion with either a constant or a changing velocity.  The average acceleration of an object is the slope of a VT graph.  Recall slope = rise/run.  Or y/x  Or /t  Therefore the slope =

 Do Model Problems on Pages 77-78  Do Practice Problems #s 1-3 on Page 80

 If the velocity time graph is a straight line (constant slope) then the object is traveling at a constant acceleration.

 However, the acceleration of objects usually changes over time.  The velocity time graph describing a changing acceleration is a curved line.

 To find the instantaneous acceleration of an object, you would find the slope of the line tangent to the curve at that instant.

 The area under the curve of a VT graph is the displacement of the object from its original position to its new position at some time ‘t’.

 Uniform or constant acceleration does not change with time.  The VT graph of constant acceleration is a straight line.  The initial velocity is and the final velocity is or you can use and.

 Recall that acceleration is the slope of the line of a VT graph:  So, if we rearrange that formula we would get:

 Distance is much easier to measure than velocity.  We have 4 equations for finding the displacement of an object but they can only be used if ACCELERATION IS CONSTANT!  This is true for most moving objects IF we ignore air resistance.

 The displacement of an object that is moving with uniform acceleration:

 The displacement of an object that starts with an initial velocity and then accelerates uniformly is found from:

 If the object starts from rest then the initial velocity is zero, therefore the previous equation can be simplified to:

 The displacement of an object when the velocity and acceleration are known can be found using:

 To find the final velocity when initial velocity, acceleration, and displacement are known, use:

 You would choose which formula to use depending on what variables you are given.  Each formula can be rearranged according to what variable you are solving for.  Do Model Problems 2 & 3 on Pages 84-87  Do Practice Problems #s 4, 6, & 7 on Page 89  Do Equations of Motion Worksheet #s 1-16

 Galileo was the first person to show that objects fall to Earth with constant acceleration.  As long as air resistance is ignored, the same acceleration due to gravity at a certain location on Earth is the same for all objects regardless of their mass and initial velocity.

 The symbol for acceleration due to gravity is.  Gravity is a vector quantity because it has size and direction.  As noted before, we have designated up as a positive direction and down as a negative direction.  Therefore all falling objects will have a negative velocity and a negative acceleration.

 On the surface of Earth, = -9.81 m/s 2. Note - Negative because of the downward direction.  However, varies, the farther you are from the surface of the Earth, the smaller gets.  Free falling objects under the force of gravity undergo uniform or constant acceleration.  As an object falls, its velocity becomes more and more negative.

 Terminal velocity is the maximum velocity at which a free falling object will fall because of air resistance.  Once it reached its terminal velocity, an object will continue to fall at this maximum velocity without change.  No change in velocity therefore no acceleration.

 During free fall, the position of the object also changes.  We can find the velocity and displacement of the object using the acceleration equations by substituting for.

 Model Problem Page 84  Do #s 17-20 on the Equations of Motion Worksheet.

 Acceleration Due to Gravity Lab  Worksheet Chapter 4 (Red Book) Problems #s 1-12  Acceleration Assignment  Acceleration Review Sheet  Chapter 3 Review Questions (Green Book) Page 116-117 #s 11-18

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