Question

A car travels a distance of 100 km in 2 hrs. Average speed of car will be :

• A. 30 m/s
• B. 0.5 m/s
• C. 13.88 m/s
• D. 13.18 m/s

Hint:

1. Calculate speed in km/hr: Speed = Distance / Time = \(100 \text{ km} / 2 \text{ hrs} = 50 \text{ km/hr}\). 2. Convert km/hr to m/s: Multiply by the conversion factor \(\frac{5}{18}\). (Because \(1 \text{ km} = 1000 \text{ m}\) and \(1 \text{ hr} = 3600 \text{ s}\), so \(\frac{1000}{3600} = \frac{10}{36} = \frac{5}{18}\)). 3. Speed in m/s = \(50 \times \frac{5}{18} = \frac{250}{18} = \frac{125}{9}\). 4. \(\frac{125}{9} \approx 13.888...\) which rounds to \(13.88 \text{ m/s}\).

Answer 1

The Correct Option is C

Concept: Average speed is calculated as the total distance traveled divided by the total time taken. Average Speed = \(\frac{\text{Total Distance}}{\text{Total Time}}\). We need to ensure units are consistent, and the final answer is required in m/s. Step 1: Identify given distance and time Distance (\(d\)) = 100 km Time (\(t\)) = 2 hours Step 2: Calculate average speed in km/hr Average Speed (km/hr) = \(\frac{100 \text{ km}}{2 \text{ hrs}} = 50 \text{ km/hr}\). Step 3: Convert km/hr to m/s To convert km/hr to m/s, we use the following conversions: 1 km = 1000 meters (m) 1 hour = 3600 seconds (s) (since 1 hour = 60 minutes, and 1 minute = 60 seconds) So, \(1 \text{ km/hr} = \frac{1 \text{ km}}{1 \text{ hr}} = \frac{1000 \text{ m}}{3600 \text{ s}} = \frac{10}{36} \text{ m/s} = \frac{5}{18} \text{ m/s}\). Therefore, to convert km/hr to m/s, multiply by \(\frac{5}{18}\). Average Speed (m/s) = \(50 \text{ km/hr} \times \frac{5}{18} \text{ m/s per km/hr}\) \[ \text{Average Speed (m/s)} = \frac{50 \times 5}{18} = \frac{250}{18} \] Step 4: Calculate the numerical value \[ \frac{250}{18} = \frac{125}{9} \] Now, perform the division: \(125 \div 9\). \(125 \div 9 \approx 13.888... \) So, Average Speed \(\approx 13.88 \text{ m/s}\) (rounded to two decimal places). This matches option (3).