INDEPENDENT VARIABLE AN OBJECT FALLS D METERS IN T SECONDS

D =f(t)

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The independent variable in the object falling scenario is time (t).

In the context of an object falling, the independent variable is typically the time it takes for the object to fall, denoted as "t" (in seconds). The dependent variable is the distance the object falls, denoted as "d" (in meters).

To determine the relationship between the independent variable (time) and the dependent variable (distance), you can perform an experiment or use a mathematical model.

Experimentally, you can drop an object from a known height and measure the time it takes to fall using a stopwatch or a motion detector. Repeat this process for multiple trials, recording the corresponding distances each time. By plotting the time (independent variable) on the x-axis and the distance (dependent variable) on the y-axis, you can visually observe the relationship.

Alternatively, you can use a mathematical model to describe the relationship between time and distance for a falling object. One such model is given by the equation:

d = 0.5 * g * t^2

Where:
- d represents the distance (in meters) the object falls,
- g is the acceleration due to gravity, which is approximately 9.8 m/s^2 on the surface of the earth,
- t is the time (in seconds) it takes for the object to fall.

Using this equation, you can plug in different values for time (t) to calculate the corresponding distances (d).

Remember, in this scenario, the independent variable is time (t), which is manipulated or chosen by the experimenter or problem-solver, while the dependent variable is the distance (d), which is measured or observed in response to changes in the independent variable.