Lecture 3:  1-Dimensional Motion
Acceleration
(1) Acceleration  Acceleration is what happens when the velocity of an object changes: it is the rate of change of velocity.  Therefore, an object with constant velocity is not accelerating since constant velocity means that the velocity does not change.  Finally, acceleration is a vector quantity, therefore, it has magnitude and direction.
                            Average acceleration is defined as the change in velocity divided by the total time elapsed.
a = Dv/Dt
                            Average acceleration is the slope of the velocity versus time graph.

(2) Instantaneous acceleration, just like instantaneous velocity, gives us the acceleration of an object for any particular time during it's motion. It also allows us to determine if the acceleration is increasing, decreasing, or zero.

Graphical Interpretation
(1) Position versus Time Graph:  Interpreting graphs is an essential to learning motion.  We begin by looking at the position versus time graph.  What type of information can we get from these position versus time graphs and how do we interpret this information?
The slope of this graph gives us valuable information about the velocity of the motion.  In fact the slope of the graph gives us the velocity of the motion.
(a) Consider the figure below.  The slope of the graph is positive therefore we can say that the velocity of the object is positive for the path shown in the figure.
(b) Consider the figure below.  The slope of the graph is negative therefore we can say that the velocity of the object is negative for the path shown in the figure.
(c) Consider the figure below.  The slope of the graph is zero therefore we can say that the velocity of the object is zero for the path shown in the figure.




(2) Velocity versus Time Graph.  From this graph, we can obtain similar information about the acceleration of the object.  With similar graphs we can say if the object has positive acceleration, negative acceleration, or zero acceleration.

(a)  The slope of the graph is positive therefore we can say that the acceleration of the object is positive for the path shown in the figure.
(b) The slope of the graph is negative therefore we can say that the acceleration of the object is negative for the path shown in the figure.
(c)  The slope of the graph is zero therefore we can say that the acceleration of the object is zero for the path shown in the figure.

(3) Motion Diagrams.  The basic motion diagram is represented by dots.  Each dot represents one second and the dots are spaced to represent the distance moved in one second.  The motion diagrams below represent some of the more basic types of motion.
(a) Uniform motion: the dots are equally spaced since the object is moving with a uniform velocity in a straight line.  That is, there is no acceleration.

(b) Accelerated motion - increasing velocity:  the dots are getting farther and farther apart indicating that the velocity of the object is increasing to the right.  This is one type of accelerated motion.
(c) Accelerated motion - decreasing velocity:  the dots are getting closer indicating that the velocity of the object is decreasing to the right.  This is another type of accelerated motion.

Motion with Constant Acceleration

Motion in the x-direction
Unless otherwise specified, for all the problems from now on, the motion involves constant acceleration. This means that the velocity increases uniformly and the change in acceleration is zero.  As a result, the following equations are used to solve a variety of problems involving motion with constant acceleration in the x-direction.
Note: The equations for average velocity and acceleration still apply.  In addition, we have the following equations of motion:
                            x = xo +vot +(1/2)at2
                            v = vo + at
                            x = xo + (1/2)(v+vo)t
                            v2 = vo2 + 2a (x - xo)

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