Final answer:
The speed of a falling object experiencing decreasing acceleration due to air resistance can be estimated by integrating the acceleration over time. With no air resistance, objects in free fall on Earth experience a constant acceleration of 9.8 m/s².
Step-by-step explanation:
In the scenario of a falling object with decreasing acceleration due to air resistance, the speed of the object at a given time can be estimated by integrating the acceleration function over time. Using the trapezoidal rule or another numerical integration method, we could find an estimate for the velocity (speed) of the object at any point in time.
On Earth, free-falling objects without air resistance have a constant acceleration due to gravity of approximately 9.8 m/s². However, air resistance affects the acceleration of real objects and causes it to decrease over time as the velocity increases, approaching the terminal velocity where the net acceleration becomes zero.
For an object in free fall with a constant acceleration and no air resistance, the velocity at a given time can be found easily. However, when air resistance is taken into account, finding the velocity at a given time becomes more complex and requires numerical methods or the solution of differential equations.