A runner completes an 850m race with two laps of the 425m track in the x-y plane centered at the origin in 1 mins, 50.6s . A runner rounds the track counterclockwise starting at the point (67.6 , 0).

Find the runner's average velocity for the race.
Find the runner's average speed for the race.

avg velocity= change displacement/time=0

avg speed= distance/time=850m/110.6s

To find the runner's average velocity for the race, we need to calculate the displacement and divide it by the time taken.

1. Calculate the displacement:
The runner starts at point (67.6, 0) and finishes at the same point, so the displacement is zero. Since displacement is a vector quantity, it measures the change in position and not the path taken.

2. Calculate the time taken:
The time taken for the race is given as 1 minute and 50.6 seconds, which can be converted to 110.6 seconds.

3. Calculate average velocity:
Since the displacement is zero, the average velocity is also zero.

Therefore, the runner's average velocity for the race is 0 m/s.

To find the runner's average speed for the race, we need to calculate the total distance covered and divide it by the time taken.

1. Calculate the total distance covered:
The runner completes two laps of the 425m track, which gives a total distance of 2 x 425m = 850m.

2. Calculate the time taken:
The time taken for the race is given as 1 minute and 50.6 seconds, which can be converted to 110.6 seconds.

3. Calculate average speed:
Average speed is calculated by dividing the total distance covered by the time taken. Therefore, the average speed for the race is 850m / 110.6s ≈ 7.69 m/s.

So, the runner's average speed for the race is approximately 7.69 m/s.