A honeybee leaves the hive, flies in a straight line to a flower 6 km away in 15 min, and then takes 15 minutes to return (also in a straight line). a.) Please find the distance travelled and displacement for the entire trip: distance travelled: 1 12 km displacement: 2 0 km b.) Please find the average speed and average velocity for the entire trip: average speed: 3 0.4 km/min average velocity: 4 0.4 km/min c.) If the bee had not flown in a straight line-- but instead with an unknown motion-- to the flower and back, which could not be determined: the average speed or average velocity

a)   d = 12 km, d = 0,  b)  v = 0.4 km / min, v = 0,  c) v = 0

Explanation:

This problem asks to find the distance and the displacement. We must emphasize that the distance is a scalar and the displacement is a vector quantity

In the exercise, the bold letters indicate vectors

a) Let's find the total distance of the trip

           d = d₁ + d₂

where d₁ is the distance to get to the flowers and d₂ is the distance to return to the hive from the flowers

             d₁ = d₂ = 6 km

             d = 12 km

we look for the displacement that is a vector quantity

          d = d₁ - d₂

since the second displacement is in the opposite direction of the first

          d = 0

b) the average speed of the trip, again this magnitude is a scalar

          v = d / t

distance is d = 12 km t total time is t = 15 + 15 = 30 min

          v = 12/30

          v = 0.4 km / min

average velocity (vector) of the entire travel, in that case the displacement is zero

          v = 0

c) If the path is not a straight line but the time is the same, the average speed cannot be calculated since it lacks the distance value

In the same case to calculate the average velocity that is a vector, it will be zero since the net displacement is zero

            v = 0

gas and liquid