Calculating Instantaneous Velocity

PAR T I: Interpreting average velocity for an object that has a uniformlychanging velocity:

  1. The data below were collected for a marble starting at rest, then rolling down an incline. Using a whole piece of graph paper and the position/time data given in the data table, make a position vs. time graph.


Answer the following questions in your notebook:

  1. What is the significance of the slope of a position vs. time graph?
  2. What is happening to the slope of your position vs. time graph as time goes on?
  3. Explain what your answers to questions 2 and 3 tell you about the motion of the marble.
  4. On the position vs. time graph, draw a line which connects the point at t= 0 to the point at t = 6.0 s.
  5. Calculate the slope of this line in the space below. Explain what the slope of this line tells you about the motion of the marble.

PAR T II: Determining the velocity at an instant in time from a graph.

  1. On your position vs. time graph, draw a line which connects the point at t = 2.0 s to the point at t = 6.0 s.
  2. Calculate the slope of this line in your notebook.
  3. Explain what the slope of this line tells you about the motion of the marble.
  4. On the position vs. time graph, draw a line which connects the point at t = 3.0 s to the point at t = 5.0 s.
  5. Calculate the slope of this line in your notebook.
  6. Explain what the slope of this line tells you about the motion of the marble.
  7. Compare the slopes you have calculated in questions 1 and 2. Explain the results of your comparison. [HIN T: You should have found the same slope.]
  8. Consider an object that speeds up uniformly. If you were to calculate the average speed of the object for a given interval of time, at what point in time would the object be traveling with an instantaneous speed equalto that average speed? If so when? Explain.
  9. Check in with your teacher before moving on to Part III.

PAR T III: Making a Velocity vs Time Graph

Using a new piece of graph paper, construct a velocity vs time graph for the motion of rolling marble following the steps below.

  1. Find the instantaneous velocity for each second of the motion using the method on the position vs time graph learned in part II.
  2. Complete the velocity columnin thedata table into your notebook:

  1. Analysis:
  2. How does the instantaneous velocity you found from the graphmethod compare with the number you would get if you simply divided the position of the object by the instant in time?
  3. Explain why simply dividing position by time isNOT thecorrect way to determine theinstantaneous velocity at each instant in time.
  4. Plot your data on a velocity vs time graph.
  5. Calculate the slope of the line on your velocity vs time graph in your notebook.
  6. Explain what the slope of this line tells you about the motion of the marble.