Accelerated Motion
Resources

Representing Motion :

Graphing

  • Uniform Motion
                Position vs. Time Graph                     Velocity vs. Time Graph


In uniform motion, the velocity stays constant. This results in:

  1. a constant slope for position Vs. time graphs
  2. a velocity Vs. time graph that is horizontal
  • Non-uniform Motion - Changing Velocity
           Position vs. Time Graph                        Velocity vs. Time Graph

In non-uniform motion, the velocity changes. This results in:

  1. a changing slope for position Vs. time graphs
  2. a velocity Vs. time graph that is not horizontal

Velocity vs. Time Graphs

What does the slope of a velocity vs. time graph tell us? The slope of a velocity vs. time graph tells us the rate of change of velocity, which we define as acceleration.

A positive slope indicates a positive acceleration. This means that over time, velocity becomes more positive.

A negative slope indicates a negative acceleration. This means that over time, velocity becomes less positive or more negative.

What does the area under a velocity vs. time graph tell us?

The area under a velocity Vs. time graph is the displacement.

For Graph 1

Graph 2

Graph 3

Area = Dd = vt

Area = Dd = 1/2vt = 1/2at2

Area = Dd = v1t + 1/2(v2 - v1)t 

= v1t + 1/2at2

Motion Maps

We can represent non-uniform motion with motion maps. In addition to velocity arrows, we can include acceleration arrows, which indicate the direction of acceleration.

Equations for linear non-uniform motion:

1) Average velocity
_
v = 1/2(v1 + v2)
 

1) Relating initial and final velocity, time and acceleration

a = (v2 - v1) / t            or          v2 = v1 + at

2) Relating displacement, initial velocity, time and acceleration

Dd =  v1t + 1/2at2

3) Relating displacement, initial and final velocity and acceleration

v22 = v12 + 2aDd

Acceleration due to Gravity

Gravity is a fundamental force that attracts any two particles that have mass. If we consider the earth as one particle, any object at the earth's surface will feel a net force towards the center of the earth. This force will always be perpendicular to the horizon. The acceleration due to gravity (g) on the earth's surface is about 9.8 m/s2. Because the moon is much less massive than the earth, the acceleration due to gravity of the moon at its surface is only about 1.6 m/s2.

When we consider free falling objects, we use the same equations we use for acceleration but we replace g for a.

Horizontal motion does not affect the acceleration due to gravity. Also gravity does not affect horizontal motion.

Some Interesting Links To Other Sites That Describe Accelerated  Motion:

http://www.mcasco.com/p1consta.html
http://dept.physics.upenn.edu/courses/gladney/mathphys/subsection1_1_2.html

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