A2L Item 059
- Description: Compare accelerations from velocity-time graphs.
- Goal: linking acceleration and velocity graphically.
- Source: UMPERG
- Keywords: Velocity, Mechanics, Graphing, Acceleration
The question for students:
The
plot of velocity versus time is shown at right for three objects. Which
object has the largest acceleration at t = 2.5s?
- Object A only
- Object B only
- Object C only
- Both B and C
- Both A and C
- Both A and B
- All three have the same acceleration at t = 2.5s
- None of the above
- Cannot be determined
Commentary for teachers:
Answer
(6) Objects (A) and (B) have the same acceleration (i.e., they have the same slope for the velocity vs. time graph at t=2.5s) Object (C) has a constant velocity (zero slope).
Background
After students have been introduced to acceleration, but before they are given a procedure for determining the acceleration from a graph of velocity vs. time. Students should answer this question after they have gained an understanding of the definition of acceleration, but before they are given any explicit instruction for how acceleration relates to a velocity vs. time graph.
Questions to Reveal Student Reasoning
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 velocity vs. time graph indicate that an object has a zero velocity? Zero acceleration? What features indicate a negative acceleration? Positive acceleration?
Suggestions
Redraw the velocity vs. time graph for object (A) twice more. In one drawing approximate the curve with three straight line segments. In the second approximate the curve with 6 straight line segments.