What is the average speed of a dog chasing a ball from t=0.0s to t=3.0s if given the position function?

To find the average speed of the dog chasing the ball over the given time interval from t=0.0s to t=3.0s, you start by determining the distance the dog travels during that time period. Average speed is defined as the total distance traveled divided by the total time taken.

If the position function is provided, you would evaluate the position of the dog at t=0.0s and at t=3.0s. The distance traveled by the dog can be calculated as follows:

1. Determine the position at t=3.0 seconds and at t=0.0 seconds.

2. Subtract the initial position from the position at t=3.0 seconds to find the total distance traveled.

3. Since the total time elapsed is 3.0 seconds, use the formula for average speed:

[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} ]

For the average speed to be 5.1 m/s, the distance traveled by the dog during that time must be 15.3 meters. Therefore, if the calculations lead you to this distance, it logically results in an average speed of 5.1 m/s.