Final answer:
The velocity of a freely falling ball five seconds after it attained a velocity of 19.6 m/s would be 68.6 m/s, considering the constant acceleration due to gravity of 9.8 m/s².
Step-by-step explanation:
If a freely falling ball has attained a velocity of 19.6 m/s after two seconds, we can assume that it is subject to earth's gravity with no other forces acting on it (like air resistance). Therefore, the acceleration due to gravity, which is 9.8 m/s², is constant throughout the ball's fall. In order to find the velocity five seconds later, we add the acceleration (9.8 m/s²) multiplied by the time span (5 seconds) to the initial velocity at the two-second mark.
Thus, the velocity after five seconds would be:
Velocity at 7 seconds = Initial velocity at 2 seconds + (Acceleration × Time interval)
Velocity at 7 seconds = 19.6 m/s + (9.8 m/s² × 5 s) = 19.6 m/s + 49 m/s
Velocity at 7 seconds = 68.6 m/s
Therefore, seven seconds after the initial observation (two seconds into free fall), the velocity of the ball would be 68.6 m/s, assuming a constant acceleration due to gravity and no other forces acting upon it.