A truck departs at 7 AM is a common scenario in motion problems. This article will guide you through solving various types of same-direction motion problems, applicable to cases where vehicles start at the same or different times.
Same-Direction Motion Problems
Case 1: Starting at the Same Time, Different Locations
Example: A truck departs from point A at 7 AM with a speed of 60 km/h. At the same time, a car departs from point B, 100 km away from A, with a speed of 80 km/h, in the same direction as the truck. How long will it take for the car to catch up with the truck?
Solution:
- Find the relative speed: The relative speed between the two vehicles is: 80 km/h – 60 km/h = 20 km/h.
- Find the time to meet: The time it takes for the car to catch up with the truck is: 100 km : 20 km/h = 5 hours.
Conclusion: The car will catch up with the truck after 5 hours.
Illustration of a truck and a car moving in the same direction, with the car starting behind the truck.
Example 2: A truck departs from Hanoi at 7 AM to Hai Phong with a speed of 50 km/h. A passenger car departs from Hung Yen, 60 km away from Hanoi, also going to Hai Phong with a speed of 70 km/h. What time will the passenger car catch up with the truck?
Solution:
- Find the relative speed: 70 km/h – 50 km/h = 20 km/h
- Find the time to meet: 60 km : 20 km/h = 3 hours
- Find the time they meet: 7 AM + 3 hours = 10 AM
Conclusion: The passenger car will catch up with the truck at 10 AM.
Case 2: Starting at Different Times, Same Location
Example: A truck departs from point A at 7 AM with a speed of 40 km/h. One hour later, a car also departs from A with a speed of 60 km/h, in the same direction as the truck. How long will it take for the car to catch up with the truck?
Solution:
- Find the distance the truck travels beforehand: In 1 hour, the truck travels: 40 km/h x 1 hour = 40 km.
- Find the relative speed: 60 km/h – 40 km/h = 20 km/h
- Find the time to meet: 40 km : 20 km/h = 2 hours.
Conclusion: The car will catch up with the truck after 2 hours (calculated from the time the car departs).
Diagram illustrating a truck and a car starting from the same point but at different times and moving in the same direction.
Conclusion
Mastering the method of calculating relative speed and initial distance is key to solving same-direction motion problems. When a truck departs at 7 AM or any other time, applying the correct formulas will help you find the time and location where the two vehicles meet.
