the difference between t = 1 and ∆t = 1

Question

for example , when i want to see how fast is time , i see the longest hand in clock , the first time i start to observe , the clock hand is pointing at 12 , then after few moment the clock hand moved once , which mean i passed 1 second , and then moved once again , which mean in total i have passed 2 second.

From that statement , is that mean i have passed 2 second ( t = 2 ) , or the difference of my current time and the time when i start to observe is 2 ? ( ∆t = | t2 - t0 | = 2 )

so is there any difference between using t = 2 and ∆t = 2 mathematically ?

If you have $t_0=0$ and $t_1=2$, then $\Delta t=2$. If you use "directly" the variable $t$ and you assume that the initial value is $0$, then after $2$ seconds you have $t=2$. — Mauro ALLEGRANZA, Sep 27 '19 at 09:48
Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to. — José Carlos Santos, Sep 27 '19 at 09:50
@Mauro ALLEGRANZA how about if the time i start to observe is 1 second later ? the initial value won't be 0 anymore . — user6668201, Sep 27 '19 at 10:10
The parameter $t$ is used as a frame of reference for measuring the physical phenomenon : you are free to choose the initial point (the $0$ value of the $t$-axis) but then you have to be consistent with the initial choice. That'all. — Mauro ALLEGRANZA, Sep 27 '19 at 10:51

score 2 · Answer 1 · answered Sep 27 '19 at 09:52

In this case, it is indeed possible to say that $\Delta t$ and $t$ are equivalent, but in general, you would use $\Delta t$ to describe the difference $t_1-t_0$, which is used if there is a process from $t=t_0$ to $t=t_1$. Some may also describe this as $t = t_0$ and $t' = t_1$.

After all, this is a notational problem, so you just need to be clear and consistent about which you use.

score 0 · Answer 2 · answered Sep 27 '19 at 16:23

0

$t$ is an absolute time and $\Delta t$ is a difference of time, say $\Delta t=t-t_0$.

But when $t_0$ happens to be $0$, then $t$ and $\Delta t$ are undiscernible.

In practice this isn't a problem.

answered Sep 27 '19 at 16:23

the difference between t = 1 and ∆t = 1

2 Answers2