**Unit 6: 1-Dimensional
Kinematics**

**Problem Set B**

**Overview:**

Problem Set B targets your ability to interpret position time plots for a motion and to use them to answer questions regarding the displacement, distance, average speed and average velocity.

Position-time graphs represent variations in an object's position
over time. Thus, an inspection of the values being plotted along the
vertical axis allows one to determine position values and changes in
position values. These axis values are related to the distance and
displacement for an object's motion. The
**displacement** of an object is
simply the overall change in position of the object; it regards only
the initial and the final position. Being a vector quantity, it
includes a direction that is often expressed as a positive or a
negative sign (for rightward and leftward). The
**distance** traveled by an object is
the accumulation of all the *ground covered*. In effect, it is
the sum of all the changes in position for each *leg* of a trip.
Being a scalar quantity, it is ignorant of direction and does not
distinguish between a change in position to the left and one to the
right. If a person walks 2 meters, left and then 6 meters right, then
the displacement is 4 meters to the right and the distance is 8
meters.

Slopes of such position-time graphs yield a ratio of the position
change to time for any specified interval of time. As such, the
slopes are equivalent to the
**velocity** of an object. Velocity
(slope in this case) is a vector quantity that has a direction
associated with it. Mathematically, the velocity direction is
represented by a positive or a negative value. Upward-sloping lines
are associated with positive velocities and downward-sloping lines
are associated with negative velocities. For an erratic motion with
multiple slopes, the average velocity can be determined by connecting
the initial and final position and calculating the slope of the
connecting line. Alternatively, the average velocity could be
determined by reading the overall position change (displacement) off
the graph and dividing by time to determine the average velocity.

The **average speed** for any
motion is simply the distance to time ratio. For a simple motion
involving a constant velocity, the average speed is simply the
absolute value of the slope. For an erratic motion with several
slopes, the average speed is the overall distance traveled divided by
the time of travel. As mentioned above, the overall distance traveled
can be determined by summing the absolute value of the individual
position changes for each *leg* of the motion.

To be successful on this problem set, you will need to be able to:

- read coordinates off a postion-time graph.
- calculate slopes of a line on a position-time graph.
- distinguish between distance and displacement.
- employ the habits of a good problem-solver.

**Additional Readings/Study
Aids:**

The following pages from The Physics Classroom tutorial may serve to be useful in assisting you in the understanding of the concepts and mathematics associated with these problems.

Calculating the Slope of a Position-Time Graph

View Sample Problem Set.

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