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A2L Item 012

Meta-Information
Description: 
Comparing accelerations of objects from their position vs. time graphs
Goal: 
Recognizing acceleration in graphs of position vs. time
Level: 
High School
Keywords: 
Acceleration
Keywords: 
Graphing
Keywords: 
Mechanics
Source: 
UMPERG

The plot of position versus time is shown for three objects. Which object has the largest acceleration at t = 2.5s?

  1. Object A only
  2. Object B only
  3. Object C only
  4. Both B and C
  5. Both A and C
  6. Both A and B
  7. All three have the same acceleration at t = 2.5s
  8. None of the above
  9. Cannot be determined
Commentary

Answer

(1); the slope of position v. time is velocity, and the slope of velocity v. time is acceleration. The only plot with a non-zero (positive) acceleration is A. Plot C denotes zero velocity, and plot B denotes a constant velocity.

Background

It is important for students to develop multiple ways of interpreting concepts. Graphical representations are often more useful than algebraic representations in solving kinematic problems. In this instance students must recognize the signature of acceleration in a plot of position vs time.

Questions to Reveal Student Thinking

How can you determine if an object is accelerating? For which objects is the velocity changing. What are some examples of objects moving according to the graphs?

What features about a position vs. time graph indicate that an object has a zero velocity? a zero acceleration? What features indicate a negative acceleration? a positive acceleration?

Suggestions

Draw a graph of velocity vs. time for each object. Then draw the graph of acceleration vs. time.

Follow up question: Can the position vs. time of an object have a negative slope at some specific time, and yet the acceleration be positive at that same time?