Final answer:
To find the time a ball takes to fall freely to a speed of 25 m/s, we use the kinematic equation, which results in approximately 2.6 seconds.
Step-by-step explanation:
To determine the time during which a ball in free fall reaches a particular speed, we use the kinematic equation for uniform acceleration, which is given by v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration due to gravity, and t is the time in seconds. In this case, since the ball is dropped from rest, the initial velocity u is 0 m/s, the acceleration a due to gravity is 9.8 m/s², and we are given the final velocity v as 25 m/s.
Rearranging the equation to solve for time t, we get t = (v - u) / a. Plugging in the values, we get t = (25 m/s - 0 m/s) / (9.8 m/s²), which calculates to approximately 2.6 seconds.
The correct choice is: The time during which the ball is in free fall is approximately 2.6 seconds.