If an object falling freely were somehow equipped with an odometer to measure the distance it travels, then the amount of distance it travels each succeeding second would be
That is physics not math.
The distance traveled each second increases due to the fact that the velocity is increasing.
If an object falling freely were equipped with an odometer to measure the distance it travels, the amount of distance it would travel each succeeding second would be different. This is because freely falling objects are subject to the force of gravity, which causes them to accelerate.
To determine the distance traveled by the object each second, you can use the equations of motion. The equation that relates distance (d), initial velocity (v0), time (t), and acceleration (a) is:
d = v0 * t + 1/2 * a * t^2
In the case of a freely falling object, the acceleration due to gravity can be considered constant and is typically denoted as "g" (approximately 9.8 m/s^2 near the Earth's surface).
So, if we assume an initial velocity of zero (since the object is dropped without an initial upward velocity), the equation simplifies to:
d = 1/2 * g * t^2
Here's how you can calculate the distance traveled by the object in each second:
1. Substitute the value of the acceleration due to gravity (g) into the equation.
2. Square the time increment (t) to calculate the time squared (t^2).
3. Multiply 1/2 times g times t^2 to determine the distance (d) traveled in each second.
For example, when the time (t) is 1 second, you can plug in the numbers and calculate:
d = 1/2 * 9.8 m/s^2 * (1 sec)^2 = 4.9 meters
So, in the first second, the object would travel approximately 4.9 meters. For each subsequent second, you would calculate the distance using the same equation, but with an increased value of time (t).