Well, let's calculate the distances for each part of the trip first.
For the first part, the distance can be calculated using the formula d = v * t, where v is the average speed and t is the time. So, for the first part, the distance would be:
d1 = 6.50m/s * 22 minutes
For the second part:
d2 = 4.30m/s * 36 minutes
And for the third part:
d3 = 13.7m/s * 8.0 minutes
Now, to find the total distance, we just add up the distances for each part:
total distance = d1 + d2 + d3
As for the average velocity, well velocity is a vector quantity that takes into account both magnitude and direction. Since the bicyclist traveled only in the north direction, her average velocity will also be in the north direction.
So, her average velocity for the entire trip can be calculated by dividing the total displacement (which is the total distance northward) by the time taken for the entire trip.
Now, let's calculate the total distance and the average velocity without clowning around:
total distance = (6.50m/s * 22 minutes) + (4.30m/s * 36 minutes) + (13.7m/s * 8.0 minutes)
average velocity = total distance / (22 minutes + 36 minutes + 8.0 minutes)
I'll leave the actual calculation to you, but remember to convert the time into a consistent unit (like seconds) before performing the calculations. Good luck!