Short Answer 
The motion of the ball begins with an initial velocity of 0 ft/s and constant acceleration, allowing for distance calculations using the formula s = (1/2)at². At t = 1s, the acceleration is determined to be 2 ft/s², enabling the distance at t = 2s to be calculated as 4 ft, leading to a distance of 3 ft traveled between 1s and 2s.
Step 1: Understand the Initial Conditions
The motion of the ball starts with an initial velocity of 0 ft/s and experiences a constant acceleration. Knowing these values is crucial for analyzing how the ball travels over time. Here we can summarize the parameters:
- Initial velocity (u) = 0 ft/s
- Acceleration = constant
Step 2: Calculate Distance Traveled at Specific Times
The formula used to calculate the distance traveled by the ball is s = ut + (1/2)at². Since the initial velocity is 0, this simplifies to s = (1/2)at². We can now compute the acceleration at time 1s while knowing the distance traveled:
- For distance s = 1 ft at time t = 1s, we find a = 2 ft/s².
- Additionally, we can calculate the distance at time t = 2s using the determined acceleration: s = 4 ft.
Step 3: Find the Distance Between Two Time Intervals
To determine how far the ball traveled between t = 1s and t = 2s, we subtract the distance traveled at 1s from the distance at 2s. This leads to a straightforward calculation:
- The distance at t = 2s is 4 ft.
- The distance at t = 1s is 1 ft.
- Therefore, the distance traveled between the two time points is s = 4 ft – 1 ft = 3 ft.