Position and Time

When describing the motion of an object, knowing where it is relative to a reference point, how fast and in what direction it is moving, and how it is accelerating (changing its rate of motion) is essential. As the object moves, the change in its position can be measured many times each second with the use of sonar. The change in position from moment to moment is expressed as velocity (meters per second). The change in velocity from moment to moment is expressed as acceleration (meters per second per second). The position of an object at a particular time can be plotted on a graph. You can also graph the velocity and acceleration of the object versus time. A graph is a mathematical picture of the motion of an object. For this reason, it is important to understand how to interpret a graph of position, velocity, or acceleration versus time. In this activity, you will analyze the graphs of position, velocity and acceleration vs. time generated by a software.

Equipment Required:

University of Colorado simulation link:

Moving Man Simulation

Lab Procedures:

For this activity, the man from the simulation will be the object in motion.

A software will plot the man's motion on a graph of position vs time, velocity and acceleration vs time respectively.

A. Position vs. Time Graphs

Procedure

Click on "Charts" and then click on the "-" signs to remove the velocity vs time and the acceleration vs time graphs.

Move the man with the cursor to the left and the right. Notice the "Play/ Stop" and "Clear" buttons.

Start with the man at x=0 and t=0

1. Move the man away from the origin to the right slowly and steadily. If the graph is a straight line, the man is moving with constant speed.
2. Use the magnifying glass buttons to "stretch" your graph's axes out so that the motion part of the graph takes up as much space as possible.
3. Pick two points on the line to calculate the slope of the position vs time graph.

slope=

Take a picture of the screen and paste it here:

Start with the man at x=0 and t=0

1. Move the man away from the origin to the left slowly and steadily.
2. Repeat steps b and c from above.

slope=

Take a picture of the screen and paste it here:

Questions:

Q1. Describe the difference between the position vs time graphs generated at parts a) and b).

Q2. What is the meaning (physics quantity and unit) of the slope in the position vs time graph?

B. Position vs time Graph and Velocity vs time Graphs

A.

Start with the man at t=0 and x=0.

Click on Charts and the "+" sign to add velocity vs time graph below the position vs time graph.

Move the man according to the description provided below.

Calculate the velocities for each time interval, type up the values in the velocity box and just pause the motion after each time interval.

A man walks 2 m to the right in 2s at constant velocity, then walks 6 m to the right at a constant velocity in 2s, then he rests for 4s. The man then turns around and walks 10 m to the left in 4s.

Paste a screen shot of the x(t) and v(t) graphs below:

For the following questions write first the equations and then complete the numerical calculations. (Include the rest time for the total time of the trip.)

1. What is the distance for the entire trip?

1. What is the displacement for the entire trip?

1. What is the average speed for the trip?
2. What is the average velocity for the trip?

B.

1. Describe the motion illustrated in the graph below using words such as position, time, speed, velocity.

2. Calculate the slope of the position vs time graph for the 5 different portions of the graph.