A runner in a relay race runs 20m north, turns around and runs south for 30 m, then turns north again and runs 40m. the entire run took 30 seconds. what was the average speed of the runner? what was the average velocity of the runner?

total distance covered: 20+30+40=90m

total time: 30s
avg speed: 90/30 = 3m/s

final displacement: 20-30+40=30m north
avg speed: 30/30 = 1 m/s north

To find the average speed and average velocity of the runner, we need to calculate the total distance covered and the total displacement.

1. Calculate the total distance covered:
The runner ran 20m north, then 30m south, and finally 40m north. Hence, the total distance covered is:
20m + 30m + 40m = 90m.

2. Calculate the total displacement:
The displacement is the straight-line distance between the initial and final positions. In this case, the runner starts and finishes in the same position, so the total displacement is zero.

3. Calculate the average speed:
Average speed is defined as total distance divided by the total time taken. Since we are given that the entire run took 30 seconds, we can calculate the average speed as:
Average Speed = Total Distance / Total Time
Average Speed = 90m / 30s
Average Speed = 3 m/s.

4. Calculate the average velocity:
Average velocity is defined as the total displacement divided by the total time taken. As mentioned earlier, the total displacement is zero, and the total time taken is 30 seconds. Thus:
Average Velocity = Total Displacement / Total Time
Average Velocity = 0m / 30s
Average Velocity = 0 m/s.

Therefore, the average speed of the runner is 3 m/s, and the average velocity is 0 m/s. The average velocity is zero because the runner ended up at the same position they started, which means their displacement is zero.

To find the average speed of the runner, we divide the total distance covered by the total time taken.

Step 1: Calculate the total distance covered.
Distance North: 20 meters
Distance South: 30 meters
Distance North: 40 meters

Total distance = Distance North + Distance South + Distance North
Total distance = 20m + 30m + 40m = 90 meters

Step 2: Calculate the total time taken.
Total time taken = 30 seconds

Step 3: Calculate average speed.
Average speed = Total distance / Total time taken
Average speed = 90m / 30s
Average speed = 3 meters per second (m/s)

Therefore, the average speed of the runner is 3 m/s.

Now, let's calculate the average velocity of the runner.

Step 4: Calculate the displacement.
Displacement is the straight-line distance between the initial and final positions, taking into account direction.

The runner started at the origin (0m) and ended 20m north. Therefore, the displacement is 20 meters north.

Step 5: Calculate the average velocity.
Average velocity = Displacement / Total time taken
Average velocity = 20m / 30s
Average velocity = 2/3 m/s north

Therefore, the average velocity of the runner is 2/3 m/s north.