- #1
mkerikss
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Homework Statement
In the answer to a homework I didn't understnad why these are the same:
d\vec{v}/dt*\vec{v}=d/dt(1/2\vec{v}*\vec{v})
Can someone explain?
Change in an expression that I don't understand
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SUMMARY
The discussion centers on the application of the product rule in vector calculus, specifically in the context of differentiating the expression \( \frac{1}{2} \vec{v} \cdot \vec{v} \). The equivalence \( \frac{d\vec{v}}{dt} \cdot \vec{v} = \frac{d}{dt}\left(\frac{1}{2} \vec{v} \cdot \vec{v}\right) \) is established through the product rule, confirming that both expressions yield the same result when differentiated. This highlights the importance of understanding vector differentiation in physics and engineering contexts.
PREREQUISITES- Understanding of vector calculus
- Familiarity with the product rule of differentiation
- Knowledge of vector dot products
- Basic principles of kinematics
- Study the product rule in vector calculus
- Explore applications of vector differentiation in physics
- Learn about the implications of vector dot products in motion analysis
- Review kinematic equations related to vector quantities
Students in physics or engineering, educators teaching vector calculus, and anyone seeking to deepen their understanding of vector differentiation and its applications.
In the answer to a homework I didn't understnad why these are the same:
d\vec{v}/dt*\vec{v}=d/dt(1/2\vec{v}*\vec{v})
Can someone explain?
- #2
cepheid
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The product rule for differentation applies, even if it is a vector dot product that is being differentiated. Therefore:
\frac{d}{dt}\left(\frac{1}{2}\vec{v} \cdot \vec{v}\right) = \frac{1}{2}\vec{v}\cdot \frac{d\vec{v}}{dt} + \frac{1}{2}\frac{d\vec{v}} {dt}\cdot \vec{v}
- #3
mkerikss
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Thank you
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