1. **State the problem:** A ball is dropped from rest and falls downward under gravity. The final velocity of the ball is 25 m/s. We need to determine the time it takes to reach this velocity. 2. **Formula used:** The velocity of an object under constant acceleration starting from rest is given by: $$v = gt$$ where $v$ is the final velocity, $g$ is the acceleration due to gravity, and $t$ is the time. 3. **Important rules:** - The acceleration due to gravity $g$ is approximately 9.8 m/s² downward. - Since the ball is dropped from rest, initial velocity $u = 0$. 4. **Calculate time:** Given $v = 25$ m/s and $g = 9.8$ m/s², $$t = \frac{v}{g} = \frac{25}{9.8}$$ 5. **Simplify the fraction:** $$t = \frac{\cancel{25}}{\cancel{9.8}} \approx 2.55 \text{ seconds}$$ 6. **Answer:** The time taken for the ball to reach 25 m/s is approximately 2.55 seconds.