How does the distance traveled by a ball in the second half-second compare to the distance in the first half-second?

The distance traveled by a ball in the second half-second compared to the first half-second increases due to the principles of uniformly accelerated motion, such as that which occurs in free fall under the influence of gravity.

During the first half-second, the ball accelerates from rest. The distance covered in this time can be calculated using the equation of motion, which states that distance is equal to the initial velocity multiplied by time plus one half of the acceleration multiplied by time squared. Since the initial velocity is zero, the distance traveled in the first half-second depends solely on the acceleration due to gravity.

As the ball moves into the second half-second, it continues to accelerate due to gravity, meaning it has gained speed since the first half-second. The ball now travels a greater distance in the second half-second because it is moving faster. This relationship illustrates the effect of constant acceleration - the longer the object moves, the greater the distance it covers as its speed increases.

This principle can be observed in various scenarios involving free-fall motion or other forms of linear accelerated motion, reaffirming that under constant acceleration, distance increases with each subsequent time interval.