To find the average speed in m/s, we need to convert the distance traveled into meters and the time taken into seconds.
Given:
Distance = 0.678 mi = 0.678 * 1609.34 m (since 1 mi = 1609.34 m)
Time = 4.00 min = 4.00 * 60 s (since 1 min = 60 s)
Average Speed = Distance / Time
Average Speed = (0.678 * 1609.34 m) / (4.00 * 60 s)
Now, we can calculate the average speed.
Average Speed = 1795.8092 m / 240 s
Average Speed ≈ 7.49 m/s
Therefore, the average speed is approximately 7.49 m/s.
To find the average velocity in m/s and the direction from the north, we need to consider both magnitude and direction.
Given:
Magnitude of displacement = 0.678 mi = 0.678 * 1609.34 m
Time = 4.00 min = 4.00 * 60 s
Average Velocity = Displacement / Time
To determine the direction from the north, we can use trigonometry. We know the starting direction is east, the bending of the track is towards the north, and halfway around the track he is running towards the west.
From the given information, we can conclude that the angle from the north will be 90 degrees clockwise.
Now, we can calculate the average velocity and the direction from the north.
Average Velocity = (0.678 * 1609.34 m) / (4.00 * 60 s)
Average Velocity ≈ 119.061 m / 240 s
Average Velocity ≈ 0.496 m/s
Therefore, the average velocity is approximately 0.496 m/s towards the west, which is 90 degrees clockwise from the north.