I've been studying classical mechanics recently and I have two (related) questions on calculus:
In the first chapter of R. Shankar's book Fundamentals of Physics, he derives vdv=adx (in a time interval [t,t+dt] as dt→0) from the definitions of a and v. Then he writes:
∫v2v1vdv=a∫x2x1dx
for the situation when v and x change in a time interval [t1,t2], and I don't quite understand how that follows (as the quantities are equal in the same time intervals, while the integration is with respect to v and x; and v as a function of v is completely different than v as a function of t).
How to justify the variable change done here? It probably flows from the answer to the first question, but maybe there's something more to be said.
No comments:
Post a Comment