In the qualifying round of the 50-yd freestyle in the sectional swimming championship, Dugan got an early lead by finishing the first 25.00 yd in 10.01 seconds. Dugan finished the return leg (25.00 yd distance) in 10.22 seconds.

a. Determine Dugan's average speed for the entire race. b. Determine Dugan's average speed for the first 25.00 yd leg of the race. c. Determine Dugan's average velocity for the entire race.

a. S = d/t = (25+25)/(10.01+10.22) = yds/s.

b. S = d/t = 25/10.01 = yds/s.

To solve this problem, we need to use the formula for average speed: speed = distance/time.

a. To find Dugan's average speed for the entire race, we need to calculate the total distance and the total time. The total distance is 50.00 yd (25.00 yd for the first leg and 25.00 yd for the return leg). The total time is the sum of the times for both legs: 10.01 seconds + 10.22 seconds = 20.23 seconds.

Using the formula, Dugan's average speed for the entire race is:

speed = distance / time
speed = 50.00 yd / 20.23 s
speed ≈ 2.469 yd/s

b. To find Dugan's average speed for the first 25.00 yd leg of the race, we need to divide the distance (25.00 yd) by the time (10.01 seconds) taken for that leg.

speed = distance / time
speed = 25.00 yd / 10.01 s
speed ≈ 2.498 yd/s

c. Average velocity is the displacement divided by the time taken. Displacement is the change in position, which is zero in this case since Dugan returned to the starting point after completing the race. Therefore, Dugan's average velocity for the entire race is zero.

To find Dugan's average speed for the entire race, we need to calculate the total distance he covered and the total time it took him.

a. Average speed is calculated by dividing the total distance by the total time. In this case, the total distance is 50.00 yards (25.00 yards for the first leg + 25.00 yards for the return leg). The total time is the sum of the times for both legs: 10.01 seconds for the first leg + 10.22 seconds for the return leg.

To find Dugan's average speed for the entire race:
Average speed = (Total Distance) / (Total Time)
Average speed = 50.00 yards / (10.01 seconds + 10.22 seconds)

b. To determine Dugan's average speed for the first 25.00 yard leg of the race, we need to divide the distance covered in the first leg by the time it took.

Average speed for the first 25.00 yard leg = (Distance covered in the first leg) / (Time taken for the first leg)

c. To determine Dugan's average velocity for the entire race, we need to calculate the displacement (change in position) and divide it by the total time taken.

Average velocity for the entire race = (Displacement) / (Total Time)

To calculate the displacement, we need to consider the direction. Since the race involves swimming back and forth in the pool, the displacement will be zero as Dugan returns to the starting point. Therefore, his average velocity will be zero.

a= 2.47 yds/s

b= 2.49 yds/s