Understanding the Concepts
* Free Fall: This means the only force acting on the stone is gravity.
* Acceleration due to Gravity (g): The acceleration due to gravity is approximately 9.8 m/s². This means the stone's velocity increases by 9.8 m/s every second it falls.
Calculations
1. Velocity after 8.0 seconds:
* Initial velocity (v₀) = 0 m/s (since it starts from rest)
* Time (t) = 8.0 s
* Acceleration (a) = 9.8 m/s²
Use the following equation:
v = v₀ + at
v = 0 + (9.8 m/s²)(8.0 s)
v = 78.4 m/s
Therefore, the velocity of the stone after 8.0 seconds is 78.4 m/s.
2. Displacement during 8.0 seconds:
* Use the following equation:
d = v₀t + (1/2)at²
* d = (0 m/s)(8.0 s) + (1/2)(9.8 m/s²)(8.0 s)²
* d = 0 + (4.9 m/s²)(64 s²)
* d = 313.6 m
Therefore, the displacement of the stone during 8.0 seconds is 313.6 meters.
Important Note: These calculations assume air resistance is negligible. In reality, air resistance would slow the stone down, resulting in a slightly lower velocity and displacement.
