Kinematic Equations: T vs Delta T vs DT

[phrygian]

You see the variables in the kinematic equations expressed as different things sometimes such as t, delta t, dt; or d, delta x, dx; What are all the different forms of the kinematic equations with these different variables? Do you approach certain problems with certain forms or can they all just be used interchangeably for each other?
Thanks for the help

 

[cosmic_tears]

Have you studied calculus?
t, delta t and dt for example are all related to time (in your example), but they are totally different, obviously.
t is usually a point in the time dimension. t=5, for example, means the point on the "t=5" axis.
delta t usually implies a difference between two time positions. if I have begun moving at t=2, and have finished my movement in t=7, then delta t is 5.
dt is when delta t is taken to be infinitisimally small. This expression is used to develop basic, more general equations in mechanics, using calculus.
Did that answer your question?

 

[phrygian]

So is this correct, the calculus is only used to derive the kinematic equations, but in kinematics problems using the kinematic equations you don't use dt or dx you use delta t and delta x?

 

[cosmic_tears]

Well, generally, and usually, physics isn't as rigorous and demanding, at least not on high school level and low degrees levels, as mathematics. However, You can't really study mechanics and understand it profoundly if you don't have the tools of calculus.
You can always solve easy problems with basic equations. More complicated problems might involve diffrential equations, for example - but they can also be solved using a "technique", rather than real mathematics. But most problems I encounter on my degree of physics include much use of calculus - not theoratical use but practical one.

delta t and delta x are very common and widly used on high school level as well. "dx" and "dt" are kinda cencored, but as you progress through university and college it becomes difficult to ignore them. There's no way you can study mechanics in a high level of detail without background in calculus.