8. make a rule: if the acceleration is constant and the starting velocity is zero, what is the relationship between the acceleration of a falling body (a), the time it takes to fall (t), and its instantaneous velocity when it hits the ground (v)?

The relationship between acceleration, velocity and time is .

Explanation:

As per the Newton's first law of motion.

Here,

Velocity at time is

Initial velocity is

Acceleration is

Time is

The initial velocity is zero. Put the for in above equation.

Thus, the acceleration of a falling body (a), the time it takes to fall (t), and its instantaneous velocity when it hits the ground (v) is .

Learn more about Law of motion here:

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In a uniform accelerated motion, the velocity at time t is given by:

where

is the initial velocity

a is the acceleration

t is the time

In this problem, we are told that the starting velocity of the body is zero (), so we can rewrite the previous equation as

and if we take t as the time the body takes to hits the ground, this relationship gives us the velocity of the body when it hits the ground.

the independent variable, or the one that is intentionally manipulated is the speed.