Acceleration for Position-time graphs

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Discussion Overview

The discussion centers around the interpretation of acceleration in relation to position-time graphs, specifically addressing how the slope of the graphs relates to the concepts of speeding up and slowing down. Participants explore the implications of negative and positive acceleration in this context.

Discussion Character

  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants note that in the first graph, the slope is negative and the object is speeding up, while in the second graph, the slope is also negative but the object is slowing down.
  • There is confusion regarding why the first graph is associated with negative acceleration and the second with positive acceleration.
  • One participant mentions that acceleration is the second derivative of position versus time, but this does not clarify the confusion for others.
  • Another participant suggests that the question may have reversed the graphs, indicating that the first graph's slope is getting steeper (speeding up) and the second's slope is getting less steep (slowing down).
  • A later reply discusses the difference between the second derivatives of different functions, suggesting that the curvature of the graphs affects the sign of the acceleration.

Areas of Agreement / Disagreement

Participants express confusion and differing interpretations regarding the relationship between the slopes of the graphs and the corresponding accelerations. No consensus is reached on the correct interpretation of the graphs.

Contextual Notes

Participants highlight the importance of understanding the nature of the slopes and derivatives, but there are unresolved assumptions regarding the definitions of acceleration in this context.

Yodaa
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Yodaa said:
1. http://www.physicsclassroom.com/Class/1DKin/U1L3a16.gif
2. http://www.physicsclassroom.com/Class/1DKin/U1L3a17.GIF

In the first graph, I get that that the slope is negative and that the object is speeding up
And in the second graph, the slope is negative and the object is slowing down
But I'm unable to understand why the first graph has negative acceleration while the second one has positive acceleration?

Your question reversed the graphs?
In the first graph, the slope is getting steeper, speed up.
In the second graph, slope is getting less steep, slowing down.
 
berkeman said:
Acceleration is the second derivative of the position versus time... :smile:
@berkeman I am sorry i don't understand how that relates to negative acceleration for the first and positive acceleration for the second:oldconfused:
 
mathman said:
Your question reversed the graphs?
In the first graph, the slope is getting steeper, speed up.
In the second graph, slope is getting less steep, slowing down.

@mathman that is exactly what i mentioned above...
 
Yodaa said:
@berkeman I am sorry i don't understand how that relates to negative acceleration for the first and positive acceleration for the second:oldconfused:

Do you understand the difference between the 2nd derivative of y=x2 and y=-x2?

Plot each of those two functions, and look at the nature of the curvature. One is curving UP, while the other is curving DOWN. So which one will give you a positive second derivative, and which one will give you a negative second derivative?

Zz.
 

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