The position of a free-falling object is measured downward from a certain starting point.

The position of the object increases with time as it falls.

The graph would be a straight line with a negative slope, starting at the initial position and ending at the final position.

Velocity vs. Time graph for a free-falling object:

The velocity of a free-falling object increases with time as it falls.

The graph would be a straight line with a positive slope, starting at zero and ending at the final velocity.

To determine the acceleration due to gravity, we can use the equation:

a = v^2/s or a = 2s/t^2

Where a is the acceleration, v is the final velocity, s is the final position, and t is the time of fall.

Since the acceleration due to gravity is constant, the slope of the velocity vs time graph is the acceleration.

Position vs. Time:

The graph for position vs. time for a free-falling object would be a straight line that starts at a non-zero position (the initial height of the object) and decreases as time goes on. The slope of this line would represent the velocity of the object. The equation for this line would be:

y = -g*t + h

where g is the acceleration due to gravity, t is the time, and h is the initial height of the object.

Velocity vs. Time:

The graph for velocity vs. time for a free-falling object would be a straight line that starts at a non-zero velocity (the initial velocity of the object) and decreases as time goes on. The slope of this line would represent the acceleration of the object. The equation for this line would be:

y = -g*t + v

where g is the acceleration due to gravity, t is the time, and v is the initial velocity of the object.

Determining the Acceleration due to Gravity:

To determine the acceleration due to gravity, we can use the slope of either the position vs. time or velocity vs. time graph. For the position vs. time graph, the slope is -g, and for the velocity vs. time graph, the slope is -g. Therefore, we can conclude that the acceleration due to gravity is -g.