What's the difference between these two formulas and how are these called?

Question

I just want to know the differences between these two formulas:

$h = h_0 + v_0 t ± \frac{1}{2} g t^2$

and

$y = y_0 + v_{0y} t + \frac{1}{2} g t^2$

Also, how are these called in English?

Answer 1

As far as I can tell, the two formulas look the same. In english, we write these formulas as:

In the horizontal (or x-direction):

$x = x_0 + v_{0x}t + \frac{1}{2}at^2$, where $x$ represents distance in the horizontal direction, $x_0$ represents the initial distance, $v_{0x}$ is the initial velocity in the x-direction (sometimes instead written as $u_x$) and finally $a$ is the acceleration in the horizontal direction.

Similarly, we have for the vertical, or y-direction:

$y = y_0 + v_{0y}t + \frac{1}{2}gt^2$

Notice I have replaced $a$ with $g$, since in most problems, the acceleration in the y-direction is due to gravity, so $a=g$.

These equations are referred to as "kinematic equations" along with these additional formulas:

$v^2 = u^2 + 2as$ and $v = u + at$.