What dimensions of (time)−2 mean ?

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SUMMARY

The discussion centers on the dimensional analysis of the equation d²x/dt² = -k/m x, where the left-hand side represents acceleration. It is established that k/m must have dimensions of (time)−2 because acceleration is defined as length divided by time squared. The conversation emphasizes the importance of understanding dimensions in physics, particularly in the context of the SI system, where length (L) is measured in meters (m) and time (T) in seconds (s). The conclusion highlights that the SI units for acceleration are meters per second squared (m/s²).

PREREQUISITES
  • Understanding of basic physics concepts, particularly Newton's laws of motion.
  • Familiarity with dimensional analysis and its significance in physics.
  • Knowledge of the SI unit system, including units for length and time.
  • Basic calculus, specifically differentiation and its application in physics equations.
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  • Study the principles of dimensional analysis in greater depth.
  • Learn about Newton's second law of motion and its mathematical representation.
  • Explore the relationship between acceleration, velocity, and displacement in physics.
  • Investigate the implications of units and dimensions in experimental physics.
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This discussion is beneficial for physics students, educators, and anyone interested in mastering the fundamentals of dimensional analysis and its application in understanding motion and acceleration.

Physou
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I am self learning Physics From a course I read the following :
" .. d^2x/dt^2 = -k/m x The left hand side is an acceleration so k/m must have dimensions of (time)−2 .. "
I understand that the left hand is acceleration but why does it imply that k/m must have dimensions of (time)−2 ? I guess I also don't understand the meaning of "dimensions" here. Thank you very much.
 
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Google for "dimensional analysis" - this is something you'll have to learn very early in your self-study.
 
Dimensional analysis and units are one of the most important things you can learn. If you always check your units you will catch a lot of mistakes.

In a system of units, each unit is considered to have some dimension. For example, in the SI system the meter (m) has the dimension of length (L) and the second (s) has the dimension of time (T).

So what are the SI units and dimensions for acceleration?
 
Thank you very much for your help, I really appreciate ! I understand now that length / time squared are the dimensions of acceleration and its SI units are m / s squared
 

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