What is the difference between t0 and ti?

[ihaveabutt]

and does this apply to everything (x0 etc)?

 

[mikelepore]

Some authors call initial time ti and call final time tf.
Some authors call initial time t0 and call final time t.

Some author call initial velocity vi and call final velocity vf.
Some authors call initial velocity v0 and call final velocity v.

Personal preference in symbols.

 

[Mk]

Having t₀ equal a nonzero value could seem strange. So maybe t_i was invented for times when we wanted to refer to the starting point as already halfway through a process.

 

[sophiecentaur]

You just have to look carefully at the definition each time, if you want to be really sure.
Sometimes, it's hard to be consistent, from publication to publication, because there are only so many symbols to go round and they are often re-used.
t₀ could be used to stand for the first of several t_ns used on an existing time line, which may have a time origin way back somewhere.