Kinematics without definite values

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SUMMARY

The discussion centers on solving kinematics problems without definite numerical values, specifically using the equations of motion: X=X0+V0t+.5at², V=V0+at, V²=V0²+2aΔX, and S=d/t. The participant expresses difficulty in manipulating these equations without specific data. Guidance is provided to approach problems by expressing answers in terms of variables such as h, d, and t, which helps avoid rounding errors. Additionally, a query regarding the determination of maximum velocity in relation to positive and negative values is addressed.

PREREQUISITES
  • Understanding of kinematic equations and their applications
  • Familiarity with concepts of velocity and acceleration
  • Basic algebraic manipulation skills
  • Knowledge of graph interpretation, particularly position vs. time graphs
NEXT STEPS
  • Practice solving kinematics problems using variable expressions instead of numerical values
  • Explore the implications of negative velocity in kinematics
  • Learn about graph analysis techniques for motion, focusing on slope interpretation
  • Review the concept of rounding and truncation errors in mathematical calculations
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Students studying physics, particularly those tackling kinematics problems, educators seeking to enhance teaching methods, and anyone interested in improving their problem-solving skills in physics without relying on specific numerical data.

JJ91284
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I've got a homework packet that I've been working on that's due tomorrow afternoon. I was planning on visiting the physics tutoring center today on campus, but everything is shut down because of the 21" of snow that we got last night.

I have 3 problems that I've been staring at for the last hour or more and I just don't know how to proceed. Normally I have no issues what so ever when data is given. These problems don't have definite numbers so I'm struggling on how to even proceed.

Any guidance on how to get going would be appreciated

Normally I use these 4 equations and I just manipulate the equations and they work great.

X=X0+V0t+.5at2
V=V0+at
V2=V02+2aΔX
S=d/t

I'm attaching 3 links so you can see my physics problems. One last question I'd like to ask just to make sure I answered another problem correctly in my packet. When a problem asks when is its velocity greatest. Do you always go with the the highest positive number, or do you factor in a negative value as well. I know speed doesn't matter which direction your going. Velocity sign (+ or -) on the other hand indicates which direction. So if you have steeper declining slope vs a lower inclining slope on a position vs time graph, would the steeper declining slope have a greater velocity?

P1
http://img20.imageshack.us/img20/7853/001vtt.jpg

P2
http://img543.imageshack.us/img543/9262/2001v.jpg

P3
http://img80.imageshack.us/img80/1522/3001hs.jpg
 
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You proceed by using the same formulas. The answers will simply be in terms of the given information (h, d, t, etc.).

Presumably the idea is to get you thinking in terms of manipulating the mathematical formulae to a final, simplified result formula before numbers are plugged in. Eventually you will appreciate that this avoids a lot of rounding and truncation errors creeping into lengthy strings of manipulations.

Why don't you take the first problem (the falling flower pot) and give us your thoughts on how to proceed. Make an attempt and we can help.
 

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