A cyclist travels 30 km north in 2 hours and then returns back to the starting point in 1.5 hours. What is the cyclist's average speed and average velocity for the entire journey?
Answer (2)
The cyclist's average speed for the entire journey is approximately 17.14 km/h, while the average velocity is 0 km/h since the displacement is zero when returning to the starting point.
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To solve this problem, let's focus on calculating two different quantities: average speed and average velocity.
1. Average Speed Average speed is defined as the total distance traveled divided by the total time taken.
Total Distance Traveled : The cyclist travels 30 km north and then returns 30 km back to the starting point. So, the total distance traveled is: Total Distance = 30 km + 30 km = 60 km
Total Time Taken : The journey north takes 2 hours, and the return journey takes 1.5 hours. Thus, the total time is: Total Time = 2 hours + 1.5 hours = 3.5 hours
Average Speed : Now, we calculate average speed using the formula: Average Speed = Total Time Total Distance = 3.5 hours 60 km ≈ 17.14 km/h
2. Average Velocity Average velocity is defined as the total displacement divided by the total time. Displacement is a vector quantity that considers only the initial and final positions, not the path taken.
Total Displacement : Since the cyclist returns to the starting point, the total displacement is 0 km.
Average Velocity : Using the formula: Average Velocity = Total Time Total Displacement = 3.5 hours 0 km = 0 km/h
In summary, the cyclist's average speed for the entire journey is approximately 17.14 km/h, while their average velocity is 0 km/h because they ended up at their starting point.
