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In the context of physics, free fall describes the motion of an object moving solely under the influence of gravity. When objects are in free fall, they experience an acceleration toward the center of the Earth due to gravity, which is approximately 9.81 m/s². This means that for every second an object is in free fall, its velocity increases by 9.81 m/s. It's important to note that free fall assumes no air resistance.

When a brick is dropped from a building, it starts from rest, meaning its initial velocity is zero. As the brick falls under the influence of gravity, it speeds up, reaching a higher velocity just before it hits the ground. Since we're dealing with a downward force, the acceleration is constant and directs towards the earth.

Kinematic equations are fundamental in understanding motion, especially in problems involving constant acceleration like free fall. These equations relate the variables of motion: displacement, velocity, acceleration, and time. They help us find unknowns when certain variables are given.

In the exercise, the equation \( y = v_i t + \frac{1}{2} a t^2 \) was used to find the height from which the brick was dropped. Because the brick is initially at rest, the equation simplifies to \( y = \frac{1}{2} g t^2 \). This relationship shows how displacement changes over time under constant acceleration. Similarly, to find velocity just before impact, the equation \( v = v_i + a t \) comes into play. With an initial velocity of zero, this simplifies to \( v = g t \). These equations become powerful tools for solving real-life motion problems.

A velocity-time graph provides insights into how an object's velocity changes over time. For an object in free fall, the velocity-time graph will show a straight line with a positive slope. This straight line reflects the constant acceleration due to gravity.

In our problem, the graph starts from the origin because the initial velocity is zero. As time progresses, the brick accelerates, and its velocity increases at a constant rate. By the time the brick hits the ground at 2.5 seconds, the graph reaches a velocity of approximately 24.53 m/s. The slope of this line is equal to the acceleration due to gravity (9.81 m/s²), visually demonstrating how gravity affects the brick's velocity.

An acceleration-time graph illustrates how acceleration changes with respect to time. In the scenario of free fall, the acceleration remains constant. Thus, the graph is depicted as a horizontal line. For the brick in the exercise, the acceleration-time graph shows a constant acceleration of 9.81 m/s², horizontally stretching across the timeline for the whole fall duration. This constancy indicates that gravity's influence doesn’t vary while the object is in motion, provided there's no air resistance. Such a graph is pivotal in understanding the uniform nature of gravitational acceleration during free fall.

A displacement-time graph portrays how the position or height of an object changes over time. In free fall, this graph typically takes the shape of a parabola.

At the start, the brick is at a height of approximately 30.66 meters. Over time, as the brick falls, its displacement from the starting point increases rapidly. This increasing rate of change creates a parabolic curve on the graph. It begins at the highest point and drops to zero at 2.5 seconds when the brick strikes the ground. This curve visually demonstrates the increasing speed of the object as it descends, highlighting the acceleration's effect on motion.