Final answer:
The average speed of a motorcyclist who travels from point A to B and back to A at different speeds is approximately 44.44 km/h, while the average velocity is 0 km/h, because the displacement for the total trip is zero.
Step-by-step explanation:
The question at hand involves finding the average speed and average velocity of a motorcyclist that drives from point A to B and returns back to A. Since the total distance traveled is the same in both directions but the speeds are different, we can use the formula for average speed which is total distance divided by total time.
For average velocity, since the displacement is zero (the start and end points are the same), the average velocity is also zero.
To find the average speed, we need to calculate the total distance and total time. Suppose the distance from A to B is 'd' kilometers. Going from A to B at 40 km/h takes d/40 hours, and returning from B to A at 50 km/h takes d/50 hours. The total time is therefore (d/40) + (d/50) hours.
The total distance is 2d kilometers (d km each way). The average speed is the total distance divided by the total time:
Average Speed = (2d) / (d/40 + d/50) = 1 / (1/40 + 1/50)
= 1 / (5/200 + 4/200) = 1 / (9/200)
= 200/9 km/h ≈ 44.44 km/h
Since the start and end points for the journey are the same, the total displacement is 0 km. Therefore, the average velocity is 0 km/h.
Among the options given, none represents this answer correctly, hence, it seems like an error has been made in the options provided.