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A2L Item 025

Meta-Information
Description: 
Examine some position/time graphs to find out which objects had a net force applied to them.
Goal: 
Relate position/time graphs to force.
Level: 
High School
Keywords: 
Dynamics
Keywords: 
Forces
Keywords: 
Graphing
Keywords: 
Mechanics
Source: 
UMPERG

Position vs. time graphs are given below for four different objects.

Which of the objects experiences a net force sometime during the time period shown?

  1. Only object A
  2. Only object B
  3. Only object C
  4. Only object D
  5. Objects B and D
  6. Objects A and C
  7. Objects B and C
  8. None of the above
  9. Cannot be determined
Commentary

Answer

(8) is the appropriate response because both C and D experience a force during the time interval. A and B have constant velocity because the slope of their x vs. t plot is constant. Some students may not realize that D experiences a force because they will reason that D has constant velocity at any given time. However, D must experience a force to change its velocity.

Background

Recognizing the signature of acceleration from a plot of position vs. time is an important skill for students to develop. Because of familiarity, they may recognize the plot of position for a falling body and reason that the object experiences a gravitational force. This question requires two logical steps. First recognizing the consequence of constant velocity and second recognizing that a change of velocity indicates acceleration and therefore force.

Questions to Reveal Student Reasoning

Which objects have constant velocity throughout the time interval?

Which of the objects has the largest speed sometime during the time interval?

Are all of the objects moving away from the origin?

Suggestions

Have students plot the velocity of each object over the same time interval.

Have students move objects in a manner in accord with the plots. This may cause them to realize when a force must be applied.