Understanding the Concepts

* Free Fall: An object in free fall experiences constant acceleration due to gravity (approximately 9.8 m/s²).

* Displacement: The change in position of an object.

* Uniform Acceleration: In this case, the acceleration is constant, allowing us to use the equations of motion.

Equations of Motion

We'll use the following equation of motion:

* *s = ut + (1/2)at²*

Where:

* *s* = displacement

* *u* = initial velocity

* *t* = time

* *a* = acceleration

Solving the Problem

1. Identify the knowns:

* *s* = 53.9 meters (distance traveled in the 6th second)

* *t* = 1 second (since we're considering only the 6th second)

* *u* = velocity at the beginning of the 6th second (we'll need to find this)

2. Find the velocity at the start of the 6th second (u):

* We know the ball is dropped from rest, so its initial velocity is 0.

* The velocity at the end of the 5th second will be the initial velocity for the 6th second.

* Use the equation: *v = u + at* (where *v* is final velocity)

* *v* = 0 + (9.8 m/s²)(5 s) = 49 m/s

3. Substitute the values into the main equation:

* 53.9 m = (49 m/s)(1 s) + (1/2)(*a*)(1 s)²

* 53.9 m = 49 m + (1/2)(*a*)(1 s)²

4. Solve for acceleration (a):

* 53.9 m - 49 m = (1/2)(*a*)(1 s)²

* 4.9 m = (1/2)(*a*)(1 s)²

* *a* = (4.9 m) / (1/2)(1 s)²

* *a* = 9.8 m/s²

Answer:

The acceleration of the ball is 9.8 m/s². This confirms that the ball is indeed in free fall and experiencing the acceleration due to gravity.