Calculating Distance Traveled by a Car in 4 Seconds at 45 km/h

To determine how far a car travels in 4 seconds at a speed of 45 km/h, we need to follow a series of steps involving unit conversions and distance calculations. This guide will walk you through the process, ensuring a clear understanding of the necessary conversions and the application of the distance formula.

Step 1: Convert Speed from km/h to m/s

The first step in solving this problem is to convert the given speed from kilometers per hour (km/h) to meters per second (m/s). Here is the conversion process:

1 kilometer (km) is equal to 1000 meters (m). 1 hour (h) is equal to 3600 seconds (s).

Given that the car is traveling at 45 km/h, we can calculate the speed in meters per second as follows:

45 km/h 45 times; 1000 m / 3600 s

After simplifying this expression:

45 km/h  12.5 m/s

Step 2: Application of the Distance Formula

The next step is to use the distance formula to find the distance traveled. The formula for distance is:

Distance  Speed times; Time

Now, we can plug in the values:

Distance  12.5 m/s times; 4 s  50 meters

Therefore, the car will travel 50 meters in 4 seconds at a speed of 45 km/h.

Alternative Methods for Speed Conversion

Let's explore a few more ways to approach the problem using different conversion factors and methods:

Direct Conversion to Decimal: Using Fractions: Unit Cancellation Method: Dividing by Time:

Direct Conversion to Decimal

To convert 45 km/h directly to m/s, you can use the deceleration factor of 5/18:

45 km/h 45 times; (5/18) m/s

This results in:

45 km/h  12.5 m/s

Using Fractions

Alternatively, you can manually divide the numbers to get the speed in m/s:

45 km/h (45,000 meters / 3,600 seconds) 12.5 m/s

Unit Cancellation Method

A more systematic approach involves using unit cancellation to convert the speed:

45 km/h times; (1,000 m/km) times; (1 h/3,600 s) 12.5 m/s

Dividing by Time

To find the speed in m/s, you can divide the total number of meters by the total number of seconds:

45,000 meters / 3,600 seconds 12.5 m/s

Finally, multiply by the time in seconds to get the distance:

12.5 m/s times; 4 s 50 meters

Conclusion

In conclusion, by converting the speed from km/h to m/s and then applying the distance formula, we can easily determine that a car traveling at 45 km/h will cover 50 meters in 4 seconds. Understanding these conversions and formulas is essential for solving similar problems related to speed, distance, and time.