ChemPhys 173/273

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:

 

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.

Meaning of Shape on a Position-Time Graph | Meaning of Slope on a Position-Time Graph

Calculating the Slope of a Position-Time Graph

 

View Sample Problem Set.

 

Problem

Description

Audio Link
1

A routine slope calculation.

2

A routine slope calculation.

3

A routine slope calculation, but often missed due to the common error of taking a y/x ratio (as opposed to delta y/delta x ratio).

4

A routine slope calculation, but often missed due to the common error of taking a y/x ratio (as opposed to delta y/delta x ratio).

5

A routine slope calculation, but often missed due to the common error of taking a y/x ratio (as opposed to delta y/delta x ratio).

6

Determining displacement from a position-time plot.

7

Determining distance from a position-time plot.

8

Determining distance from a complicated position-time plot.

9

Finding the greatest velocity value for a complicated position-time plot; must compare several slope values.

10

Using an understanding of displacement to determine the instant in time in which an object is most displaced from the starting position.

11

Understanding the meaning of fast and relating it to a the slope position-time plot for two different objects; complex analysis.

12

Understanding the meaning of average velocity and relating it to a complicated position-time plot.

13

Understanding the meaning of average velocity and relating it to a complicated position-time plot.

14

Several lines on a position-time graph are provided; the objects which are speeding up must by identified.

15

Several lines on a position-time graph are provided; the object which is moving with the greatest magnitude of velocity must be identified.

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