Final answer:
To determine the velocity of the ball after 15 seconds, you can use the constant acceleration calculated from the data points provided. The ball accelerates at 0.5 m/s², leading to a final velocity of 7.5 m/s after 15 seconds.
Step-by-step explanation:
The student is asking about the velocity of a rolling ball after 15 seconds given a constant acceleration.
Since the table provided indicates a constant increase in velocity of 0.5 m/s every second, we can use this to find the velocity after 15 seconds.
The initial velocity is 0 m/s, and after 1 second it's 0.5 m/s, after 2 seconds it's 1 m/s, and so on. This pattern shows a linear increase, which implies a constant acceleration.
Assuming the acceleration is constant, at time t seconds, the velocity v in m/s can be calculated as v = at, with a being constant acceleration.
To calculate the acceleration, we can use any of the given velocity-time data points.
For example, at t = 1 second, v = 0.5 m/s, so a = v/t = 0.5 m/s².
Using this acceleration, the velocity after 15 seconds is v = a * t = 0.5 m/s² * 15 s = 7.5 m/s.
Therefore, the velocity of the ball relative to the surface it traveled on after 15 seconds would be 7.5 m/s, assuming the same acceleration is maintained over time.