Tuesday, May 21, 2019

kinematics - Is $dfrac{dx}{dt}$ a fraction or not?


I am new to calculus and during my mathematics class my sir defined $\dfrac{dx}{dt}$ as $$dx/dt=\lim_{t\to t_1}\dfrac{f(t)-f(t_1)}{t-t_1}$$ and my sir made a clear statement that




$\dfrac{dx}{dt}$ is not a fraction it only behaves like a fraction!



(it means $\dfrac{dx}{dt}$ is just a notation to represent that big limit!) and he made a statement that



$dx$ or $dt$ does not have any meaning it is just $\dfrac{d}{dt}(x)$ which has meaning but we treat it as $\dfrac{dx}{dt}$.



but at same time my physics sir, to derive velocity he stated



let the particle be at position $x$ at time $t$ and after an infinitesimal change in position and time it reaches $x+dx$ at time $t+dt$. Now velocity is $\dfrac{displacement}{time}$ , so we will get $v=\dfrac{dx}{dt}$




and this expression purely tells that $\dfrac{dx}{dt}$ is a fraction!


Now i don't know who is correct, so please help!




No comments:

Post a Comment

classical mechanics - Moment of a force about a given axis (Torque) - Scalar or vectorial?

I am studying Statics and saw that: The moment of a force about a given axis (or Torque) is defined by the equation: $M_X = (\vec r \times \...