from which equations is the following equation derived from:

length=(time^2 * g)/4

The equation you provided, length = (time^2 * g)/4, seems to be a formula for calculating the length of a fall or the distance traveled during free fall. It represents the relationship between time (t) squared, and the acceleration due to gravity (g), and a constant factor of 1/4.

However, it is important to note that equations are derived based on various physical principles and mathematical relationships. Without any further context or information, it is difficult to determine the exact equations from which this specific equation is derived.

In general, equations related to free fall and distance traveled can be derived based on the principles of classical mechanics, specifically kinematic equations. The most commonly used equation for distance or displacement in free fall is:

d = (1/2) * g * t^2

where d represents the distance, g is the acceleration due to gravity, and t is the time.

In your equation, it seems that the distance traveled is further divided by a factor of 4, which modifies the relationship between time squared (t^2) and gravity (g).

To derive the specific equation you provided, more information about the context or derivation process would be needed.