Does v represent speed in kinetic energy formula?

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SUMMARY

The discussion clarifies that in the kinetic energy formula (KE = (1/2)mv²), the variable 'v' can represent both speed and velocity. When treated as a scalar, 'v' is used in scalar multiplication to compute v². Conversely, if 'v' is considered a vector, the vector dot product (v·v) yields the same result for kinetic energy. This dual interpretation is valid due to the scalar nature of kinetic energy measured in joules.

PREREQUISITES
  • Understanding of kinetic energy and its formula
  • Familiarity with scalar and vector quantities
  • Basic knowledge of vector operations, including dot products
  • Concept of units in physics, specifically joules
NEXT STEPS
  • Research the differences between scalar and vector quantities in physics
  • Learn about the implications of using scalar versus vector in kinetic energy calculations
  • Study vector operations, particularly the dot product and its applications
  • Explore the concept of energy in different forms and its measurement in joules
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Physics students, educators, and anyone interested in understanding the principles of kinetic energy and the mathematical representations of speed and velocity.

Mr Davis 97
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Since kinetic energy is in is a scalar quantity in joules, then is the v in (1/2)mv2 speed or velocity?
 
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Mr Davis 97 said:
Since kinetic energy is in is a scalar quantity in joules, then is the v in (1/2)mv2 speed or velocity?
Either will work. If it is taken as a scalar then you would use scalar multiplication to compute v2 If it is taken as a vector then the vector dot product ##v{\cdot}v## will produce the same result.
 

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