The kinematic equations are:
V + at = V
V^2 + 2aS = V^2
S+vt+(1/2)at^2 = S
these 3 equations are the 'math' way of saying basically this:
event 1 = event 2,
so lets take the actual kinematic equation above and see how it is like the 'event' equation I just told you
event 1 = event 2
v + at = v
can you see how the "v + at" is on the same side as the 'event 1' part? and how 'v' on the other side of the = sign lines up on the same side as the event 2 part? So, what we are saying is that these variables from event one, when added and multiplied this way will equal the velocity of event 2.
so we will use the "_1" to refer to event 1 and "_2" to refer to event 2. now our kinematic equation looks like this:
v_1 + a_1 * t_1 = v_2
now if I were to describe the equation I would say, "velocity at event 1 plus acceleration at event 1 times time at event 1 equals velocity at event 2"
we need to add one more symbol onto our "_1" and "_2" symbols, it is direction of x and y. These equations only work when we use the numbers of a movement in the same direction. so if event 1 values were all movements in the y direction, then event 2 will be a value of movement in the y direction also.
we will use the notation of "_1y" and "_2y" which now will mean, 'event 1 in the y direction' and the other will mean 'event 2 in the y direction'