A ball initially at rest is dropped from a height and takes 5 seconds to reach the ground. What is the average speed during its fall? (g = 10 m/s²)

The correct option is 25 m/s.

To find the average speed of the ball during its fall, we can use the formula for average speed:
$$\text{Average Speed}=\frac{\text{Total Distance}}{\text{Total Time}}$$
where we first need to determine the total distance covered by the ball during its fall.

Since the ball is dropped from rest, its initial velocity ($u$) is:
$$u=0\text{ m/s}$$
The time taken ($t$) to reach the ground is 5 seconds, and the acceleration due to gravity ($g$) is given as 10 m/s².

We can use the second equation of motion to calculate the total distance ($s$) fallen by the ball:
$$s=ut+\frac{1}{2}g{t}^2$$
Substituting the given values:
$$s=(0)(5)+\frac{1}{2}(10){(5)}^2$$
$$s=0+5\times 25$$
$$s=125\text{ m}$$
So, the total distance covered by the ball during its fall is 125 meters.

Now, we can calculate the average speed:
$$\text{Average Speed}=\frac{125\text{ m}}{5\text{ s}}=25\text{ m/s}$$
Therefore, the average speed of the ball during its fall is 25 m/s.