Final answer:
The average velocity for the first portion of the trip is 24 km/h, while walking back it's 12 km/h. The average velocity for the entire trip is 0 km/h because the displacement is zero. The average speed for the entire trip is 16 km/h.
Step-by-step explanation:
To calculate the average velocity and average speed of the runner, we need to consider both the distance covered and the direction of motion.
A) Average Velocity for the First 5.0 Minutes
The runner covers 2.0 km in 5.0 minutes. Since velocity includes direction, and the runner is moving away from the starting point, the average velocity is positive. Converting minutes to hours (5.0 minutes = 1/12 hour) we get:
2.0 km / (1/12 hour) = 24 km/h
B) Average Velocity for the Time Spent Walking
Walking back to the starting point covers the same distance in 10.0 minutes (or 1/6 hour), so the average velocity is:
2.0 km / (1/6 hour) = 12 km/h.
C) Average Velocity for the Entire Trip
Since the runner ends up at the starting point, the total displacement is 0 km. Thus, the average velocity for the entire trip is also 0 km/h, regardless of the time taken.
D) Average Speed for the Entire Trip
The total distance covered is 2.0 km out and 2.0 km back, for a total of 4.0 km. The total time is 5.0 + 10.0 = 15.0 minutes, or 1/4 hour. The average speed is therefore:
4.0 km / (1/4 hour) = 16 km/h