Calculating Distance Traveled by a Car at Constant Speed
Understanding the principles of motion and speed is crucial for various real-world applications. One common problem involves calculating the distance traveled by a car moving at a constant speed. In this article, we'll solve an example problem step-by-step and explore the underlying concepts.
Word Problem: Distance Calculation Example
A car travels at a constant speed and covers 90 kilometers in 50 minutes. We need to determine the distance it would travel in 2 hours and 30 minutes at the same constant speed. Let's break this down step-by-step.
Step 1: Convert Time to Hours
First, we need to convert the given time from minutes to hours.
50 minutes 50 / 60 hours 5 / 6 hours
Step 2: Calculate the Speed of the Car
Speed is the distance traveled per unit of time. We can use the formula:
Speed Distance / Time
Speed 90 km / (5 / 6) hours
Multiplying by the reciprocal of the denominator:
Speed 90 * (6 / 5) km/h 108 km/h
Step 3: Convert the Desired Time to Hours
Next, we convert 2 hours and 30 minutes to hours.
2 hours and 30 minutes 2.5 hours
Step 4: Calculate the Distance Traveled
Finally, we use the formula for distance:
Distance Speed * Time
Substituting the values:
Distance 108 km/h * 2.5 hours 270 km
Therefore, the car will travel 270 kilometers in 2 hours and 30 minutes at the same constant speed.
Real-World Applications and Considerations
Understanding these calculations is crucial in a variety of fields, including transportation, engineering, and physics. It also helps in planning and scheduling, ensuring that travel times and distances are accurately estimated.
Common Mistakes and Clarifications
It's important to pay attention to units and conversions. For instance, in the given problem, the convertion from 90 kpm (kilometers per minute) to kph (kilometers per hour) was incorrect. The correct speed would be:
90 kpm * 60 minutes/hour 5400 kph
The speed of 5400 kph, or Mach 5.1, is unrealistic for a land vehicle. Therefore, for practical purposes, the car would be traveling at:
Speed 90 km / (5 / 6) hours 108 km/h
The distance problem was later simplified correctly to 270 kilometers.
Additional Tips and Tools
Using online calculators and tools can help verify your calculations. Additionally, checking units and making sure conversions are correct is essential.
Conclusion
By understanding and practicing these calculations, we can better estimate and plan travel times and distances. This skill is valuable in numerous practical scenarios and helps in developing a stronger grasp of the fundamentals of motion and speed.