A car runs at the rate of 20 km/hour for the first 30 km, at 25 km/hour for the next 30 km, and at 30 km/hour for the last 30 km. Calculate the average speed of the car.

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Points to Remember:

  • Average speed is calculated by total distance divided by total time.
  • Time taken for each segment of the journey needs to be calculated individually.
  • Units must be consistent throughout the calculation.

Introduction:

This question requires a factual and analytical approach to calculate the average speed of a car given varying speeds over different distances. Average speed, unlike average velocity, is a scalar quantity and only considers the magnitude of speed, not direction. It’s a crucial concept in physics and everyday life, helping us understand the overall rate of travel.

Body:

1. Calculating Time for Each Segment:

To calculate the average speed, we first need to determine the time taken for each segment of the journey. We can use the formula: Time = Distance / Speed.

  • Segment 1 (20 km/hour for 30 km): Time = 30 km / 20 km/hour = 1.5 hours
  • Segment 2 (25 km/hour for 30 km): Time = 30 km / 25 km/hour = 1.2 hours
  • Segment 3 (30 km/hour for 30 km): Time = 30 km / 30 km/hour = 1 hour

2. Calculating Total Time and Total Distance:

  • Total Time: 1.5 hours + 1.2 hours + 1 hour = 3.7 hours
  • Total Distance: 30 km + 30 km + 30 km = 90 km

3. Calculating Average Speed:

Average speed is calculated by dividing the total distance by the total time.

  • Average Speed: 90 km / 3.7 hours ≈ 24.32 km/hour

Conclusion:

The average speed of the car for the entire journey is approximately 24.32 km/hour. This calculation demonstrates the importance of considering the time taken at different speeds when determining the overall average speed. While the car traveled at speeds ranging from 20 km/hour to 30 km/hour, the average speed reflects a balanced representation of the entire trip. This simple calculation highlights the practical application of basic physics principles in everyday scenarios. Understanding average speed is crucial for efficient travel planning, logistics, and various other applications requiring accurate estimations of travel time. Further analysis could involve considering factors like traffic, road conditions, and rest stops to create a more realistic model of travel time.

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