A vehicle moves along a straight line and covers a distance of 2 km. In the first 500 m, it moves with a speed of 10 m/s and in the next 500 m, it moves with a speed of 5 m/s. With what speed should it move the remaining distance so that the journey is complete in 200 s? What is the average speed of the vehicle for the entire journey?
This problem requires applying the relationship between speed, distance, and time.
First, the total distance is converted: 2 km = 2000 m. The time for each segment is calculated using Time = Distance/Speed.
For the first 500 m: Time₁ = 500 m / 10 m/s = 50 s. For the next 500 m: Time₂ = 500 m / 5 m/s = 100 s.
The remaining distance is 2000 - 500 - 500 = 1000 m. The remaining time is 200 - 50 - 100 = 50 s.
The required speed for the remaining distance = Distance/Time = 1000 m / 50 s = 20 m/s.
The average speed = Total distance / Total time = 2000 m / 200 s = 10 m/s (or 36 km/h).
Answer: The vehicle should move at a speed of 20 m/s for the remaining distance, and the average speed for the entire journey is 10 m/s (or 36 km/h).
Explanation
This problem requires applying the relationship between speed, distance, and time from the chapter. First, calculate the time taken for each segment using Time = Distance/Speed. Then determine the remaining time and distance to find the required speed for the last segment. Average speed is calculated as total distance divided by total time.
Solution Steps
Step 1: Convert total distance: 2 km = 2000 m
Step 2: Calculate time for first 500 m: Time₁ = Distance/Speed = 500 m / 10 m/s = 50 s
Step 3: Calculate time for next 500 m: Time₂ = 500 m / 5 m/s = 100 s
Step 4: Calculate remaining distance: 2000 - 500 - 500 = 1000 m
Step 5: Calculate remaining time: 200 - 50 - 100 = 50 s
Step 6: Calculate required speed for remaining distance: Speed = Distance/Time = 1000 m / 50 s = 20 m/s
Step 7: Calculate average speed: Total distance / Total time = 2000 m / 200 s = 10 m/s
Step 8: Convert to km/h: 10 m/s × 3.6 = 36 km/h