The discussion centers on the derivation of kinetic energy from work, specifically using the equation W = ∫ F dr and the transformation involving momentum (dp/dt) and velocity (v). The participant presents a concise derivation in four lines, contrasting it with a textbook approach that spans seven lines. The conversation highlights the balance between mathematical rigor and brevity, emphasizing that while terseness may appeal to some, it can lead to confusion for students unfamiliar with the concepts involved.
PREREQUISITESThis discussion is beneficial for physics students, educators teaching introductory mechanics, and anyone interested in the mathematical foundations of kinetic energy and work. It provides insights into effective teaching methods and the importance of clarity in mathematical derivations.
Arman777 said:My book does this in 7 lines mine took 4. I don't know why books sometimes does things in long way.
There's a bit of personal taste involved here; what one person considers admirable terseness another may consider skipping important steps.Arman777 said:My book does this in 7 lines mine took 4. I don't know why books sometimes does things in long way.
Well yes you are right. Thanks for your replyNugatory said:There's a bit of personal taste involved here; what one person considers admirable terseness another may consider skipping important steps.
With textbooks an additional consideration is that skipping steps can be a problem for a student who isn't already familiar with the concept. For example, someone taking intro physics concurrently with their first calculus course may have seen their first integral just a few weeks back - it's easy to imagine that your cavalier treatment of the bounds of integration would confuse them.
For what it's worth... I understand your derivation just fine but it's not what I'd be writing on a chalkboard in front of a class.