AccelerationPhysics 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/s2, that tells how many meters per second the velocity changes every second.

Acceleration

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 =

Velocity Time Graphs

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 .

Finding Velocity with Constant Acceleration

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.

Finding Displacement with Constant Acceleration

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

4 Equations(Displacement with Constant 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.

Acceleration Due to Gravity

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/s2. 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.

Terminal Velocity

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