Acceleration Physics 521 Section 2 4 and Chapter

Acceleration Physics 521 Section 2. 4 and Chapter 3

Acceleration � 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.

Velocity Time Graphs � 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’.

Finding Velocity with Constant Acceleration � 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:

Finding Displacement with Constant Acceleration � 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.

4 Equations (Displacement with Constant Acceleration) � 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

Acceleration Due to Gravity � 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 � 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