#V_i# is the velocity of the object at that instant or *instantaneous velocity.*

#lim t to 0# states that the time we are observing the velocity is limited, and is now so short, that it is approaching #0.000000 sec#

#((triangled)/(trianglet))# informs us that the velocity is a function of the distance divided by the time, and since we are considering velocity here the direction must also be defined.

The #triangle'#s tell us the function refers to the *change in* something, in this case the *change in distance* divided by *the change in time.*

As you might suspect, since the #trianglet# observing time is so short, the #triangled# distance travelled will also be short compared to the overall distance travelled. As a result, we can be sure that the calculation of the instantaneous velocity will be correct for the moving object, which may be either accelerating, decelerating, or moving at a constant velocity.

Here is more:

https://www.brightstorm.com/science/physics/linear-and-projectile-motion/physics-instantaneous-velocity/