Lecture 2:  1-Dimensional Motion

Velocity, Speed, Displacement and Distance
(1) Scalar Quantity - a number or just the magnitude of a given quantity.

(2) Vector Quantity - a quantity that specifies both a magnitude and a direction.

(3) Position - the position of an object is the location of the object in space.  It answers the question "Where is the object?"

(4) Distance- is a SCALAR quantity. It only has magnitude and is always a positive number.  It just refers to the number of feet, meters, miles a particular trip regardless of the direction changes that ocurred during the trip.  It answers the question "How far did you go?"

(5) Displacement - is a VECTOR quantity. It has both magnitude and direction and can be a negative or a positive number. In one dimension, positive and negative give the direction of the displacement vector. Displacement is denoted by Dx = xf - xi .  The displacement answers the question "How far did you end up relative to your starting position?"  It depends on the initial and final position of a particular trip or path.  So you need to identify the initial and final positions of a particular trip.

                  Example:A man walks 70 m east then 30 m west, what is the total distance he traveled and what is his total displacement?
                    Total distance = 30 m + 70 m = 100 m
                    Displacement:  xi = 0 since he starts from the origin, xf is where he finally ends up relative to some coordinate system (see figure below).  He starts from the origin, goes 70 m to the right (+70 m), then moves to the left for 30 m (-30 m).  From the figure, he ends up at xf = 40 m, therefore:

  Dx = xf - xi = 40 m - 0 = 40 m
(6) Average speed or speed is a SCALAR quantity.  It is defined as the total distance traveled, divided by the total time elapsed.
v = d/t where d = total time and t = total elapsed time

(7) Average velocity or velocity is a VECTOR quantity, therefore it has both magnitude and direction. The average velocity is the slope of the position versus time graph.  It is defined as the total displacement divided by the total time elapsed:

average velocity = Dx/Dt
                  Example:  Consider the previous example. A man walks 70 m east in a time of 20 s then 30 m west in a time of 10 s, what is the average speed and average velocity?
                    Average speed = 100 m/ 30s = 3.33 m/s
                    Average velocity = 40 m/30 s = 1.33 m/s due East.

(8) Instantaneous Velocity  Instantaneous velocity is the average velocity over an infinitesimally (or very small) time interval.  It allows us to determine the velocity of an object at any given time unlike Average velocity which gives us the velocity over an interval of time.   Instantaneous velocity allows us to determine whether the velocity of an object is increasing, decreasing or zero at any given instant.  Therefore for any given position versus time graph, we can determine if the velocity of the object is increasing, decreasing, or zero.

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