The runner's speed increased steadily over the first two seconds of the race. The table shows the elapsed time and corresponding speed: Time (sec): 0 | 0.5 | 1 | 1.5 | 2 Speed (ft/sec): 0 | 5.1 | 9.3 | 12.5 | 15.6 To estimate the distance traveled during these two seconds, we use the speed at the end of each interval: Distance traveled = Sum of (Average speed of the interval * Time duration of the interval) From 0 to 0.5 seconds: Average speed = (0 + 5.1) / 2 = 2.55 ft/sec Distance = 2.55 ft/sec * 0.5 sec = 1.275 ft From 0.5 to 1 second: Average speed = (5.1 + 9.3) / 2 = 7.2 ft/sec Distance = 7.2 ft/sec * 0.5 sec = 3.6 ft From 1 to 1.5 seconds: Average speed = (9.3 + 12.5) / 2 = 10.9 ft/sec Distance = 10.9 ft/sec * 0.5 sec = 5.45 ft From 1.5 to 2 seconds: Average speed = (12.5 + 15.6) / 2 = 14.05 ft/sec Distance = 14.05 ft/sec * 0.5 sec = 7.025 ft Total distance traveled = 1.275 ft + 3.6 ft + 5.45 ft + 7.025 ft Total distance traveled = 17.35 ft None of the provided choices (A through E) matches the estimated distance of 17.35 ft calculated using the method provided. Please verify the choices or the estimation method.

To calculate the distance traveled during the first two seconds of the race using the speeds given at the end of each interval, we will first find the average speed during each interval and then multiply it by the time duration of that interval. Here are the steps:

1. Calculate the average speed for each time interval by averaging the given speeds at the beginning and end of the interval.

2. Multiply the average speed of each interval by the duration of that interval to find the distance covered in each interval.

3. Add up the distances covered in all intervals to find the total distance traveled in the first two seconds.

Let's do the calculation based on the above given steps:

1. From 0 to 0.5 seconds: Average speed = (0 + 5.1) / 2 = 2.55 ft/sec Distance = 2.55 ft/sec * 0.5 sec = 1.275 ft

2. From 0.5 to 1 second: Average speed = (5.1 + 9.3) / 2 = 7.2 ft/sec Distance = 7.2 ft/sec * 0.5 sec = 3.6 ft

3. From 1 to 1.5 seconds: Average speed = (9.3 + 12.5) / 2 = 10.9 ft/sec Distance = 10.9 ft/sec * 0.5 sec = 5.45 ft

4. From 1.5 to 2 seconds: Average speed = (12.5 + 15.6) / 2 = 14.05 ft/sec Distance = 14.05 ft/sec * 0.5 sec = 7.025 ft

Now we will sum these distances to get the total distance traveled during the first two seconds:

Total distance traveled = 1.275 ft + 3.6 ft + 5.45 ft + 7.025 ft Total distance traveled = 17.35 ft

The estimated distance using the average speed method for the given time intervals is 17.35 feet.