A man walks 3 miles east in 1 hour at a constant velocity, then walks 2 miles east at a constant velocity in 20 minutes, then 2 miles east at a constant velocity in 40 minutes, then rests for 1 hour and then turns around and walks 8 miles west in two hours.What is the distance,displacement, average speed, and average velocity.
To find the distance, displacement, average speed, and average velocity of the man's journey, let's break it down step by step.
1. Distance: The distance is the total path traveled by the man. We can simply add up the distances covered in each segment of the journey.
Distance = 3 miles + 2 miles + 2 miles + 8 miles
Distance = 15 miles
So, the total distance covered is 15 miles.
2. Displacement: Displacement is the shortest path from the initial position to the final position. Since the man walks east and then later west, we need to consider the direction when calculating displacement.
Displacement = (total distance traveled east) - (total distance traveled west)
Total distance traveled east = 3 miles + 2 miles + 2 miles
Total distance traveled east = 7 miles
Total distance traveled west = 8 miles
Displacement = 7 miles - 8 miles
Displacement = -1 mile
So, the displacement is -1 mile, indicating that the man ended up 1 mile to the west of the starting point.
3. Average Speed: Average speed is the total distance traveled divided by the total time taken.
Total time = 1 hour + 20 minutes + 40 minutes + 1 hour + 2 hours
Total time = 5 hours
Average speed = Distance / Time
Average speed = 15 miles / 5 hours
Average speed = 3 miles per hour
Therefore, the average speed is 3 miles per hour.
4. Average Velocity: Average velocity takes the direction into account and is calculated as the displacement divided by the total time taken.
Average velocity = Displacement / Time
Average velocity = -1 mile / 5 hours
Average velocity = -0.2 miles per hour
So, the average velocity is -0.2 miles per hour (westward).
To summarize:
- Distance: 15 miles
- Displacement: -1 mile (westwards)
- Average speed: 3 miles per hour
- Average velocity: -0.2 miles per hour (westward)