How to Calculate the Distance Covered by a Bus at 90 km/h in 20 Seconds

Introduction

Understanding how to calculate the distance covered by a bus traveling at a given speed is an essential skill, especially for individuals involved in traffic management, transportation, and even students studying physics and mathematics. In this article, we will walk through the process of determining the distance a bus traveling at 90 km/h will cover in 20 seconds, using different methods and mathematical conversions.

Method 1: Using Speed and Time Conversion

First, let's convert the speed from kilometers per hour (km/h) to meters per second (m/s). The conversion factor is as follows:

1 km/h 1000 m / 3600 s 5/18 m/s

To convert 90 km/h to m/s:

90 km/h 90 × (5/18) m/s 25 m/s

Now, we use the formula for distance:

Distance (d) Speed (v) × Time (t)

Given: v 25 m/s, t 20 seconds

d 25 m/s × 20 s 500 meters

Converting 500 meters to kilometers:

500 meters 0.500 kilometers (km)

Method 2: Using Direct Speed Conversion

Instead of converting speed, we can use the combined speed and time formula directly:

Distance (d) Speed (v) × Time (t)

Given: v 90 km/h, t 20/3600 hours (since 1 hour 3600 seconds)

First, convert the time to hours:

20 seconds 20 / 3600 hours 1/180 hours

Now, use the formula:

Distance 90 km/h × 1/180 hours 0.500 kilometers (km)

Method 3: Using Time Reduction in Minutes and Seconds

Another approach involves reducing the time to a fraction of a minute. We know:

1 hour 60 minutes, and 1 minute 60 seconds. Therefore, 90 km/h is equivalent to 1.5 km/minute.

20 seconds is 1/3 of a minute, so the distance covered:

Distance 1.5 km/minute × 1/3 minute 0.500 kilometers (km)

Summary and Additional Calculations

No matter which method is used, the distance covered by a bus traveling at 90 km/h in 20 seconds is consistently calculated to be 0.500 kilometers (km).

Alternative Methods:

1. Converting speed to m/s and using the distance formula directly. 2. Converting time to hours and then using the distance formula. 3. Reducing the time to a fraction of a minute and using the speed in km/h.

These methods provide flexibility in solving similar problems and can be used based on the available information and ease of calculation.