Calculating Speed: Distance, Time, and Unit Conversion

This problem asks us to find the speed of Rohit, given the distance he covers and the time taken. We are given the distance in kilometers (km) and the time in hours, but the options for speed are in meters per second (m/s). Therefore, we will first calculate the speed in km/h and then convert it to m/s.

Understanding the Speed, Distance, and Time Relationship

The relationship between speed, distance, and time is given by the formula:

$\text{Speed} = \frac{\text{Distance}}{\text{Time}}$

In this problem, we have:

• Distance = 1188 km
• Time = 22 hours

Calculating Rohit's Speed in km/h

Using the formula, we can calculate Rohit's speed in kilometers per hour:

$\text{Speed in km/h} = \frac{1188 \text{ km}}{22 \text{ hours}}$

Let's perform the division:

$1188 \div 22 = 54$

So, Rohit's speed is 54 km/h.

Converting Speed from km/h to m/s

The options are given in meters per second (m/s), so we need to convert 54 km/h to m/s. To do this, we use the conversion factors:

• 1 km = 1000 meters
• 1 hour = 3600 seconds

So, 1 km/h can be converted to m/s as follows:

$1 \text{ km/h} = \frac{1 \text{ km}}{1 \text{ hour}} = \frac{1000 \text{ meters}}{3600 \text{ seconds}} = \frac{1000}{3600} \text{ m/s} = \frac{10}{36} \text{ m/s} = \frac{5}{18} \text{ m/s}$

Therefore, to convert speed from km/h to m/s, we multiply by $\frac{5}{18}$.

Now, let's convert 54 km/h to m/s:

$\text{Speed in m/s} = 54 \text{ km/h} \times \frac{5}{18} \text{ m/s per km/h}$

$\text{Speed in m/s} = \frac{54}{1} \times \frac{5}{18}$

We can simplify this by dividing 54 by 18:

$54 \div 18 = 3$

Now, multiply the result by 5:

$\text{Speed in m/s} = 3 \times 5 = 15$

So, Rohit's speed is 15 m/s.

Final Speed Result

Rohit's speed is 15 m/s. Let's compare this with the given options:

• Option 1: 54 m/s
• Option 2: 25 m/s
• Option 3: 15 m/s
• Option 4: 48 m/s

The calculated speed of 15 m/s matches Option 3.

Revision Table: Speed, Distance, and Time Formulas

Additional Information on Unit Conversions

Converting between different units of speed is a common requirement in physics and mathematics problems. Here's a quick summary of important conversions:

• To convert km/h to m/s: Multiply the speed in km/h by $\frac{5}{18}$.
• To convert m/s to km/h: Multiply the speed in m/s by $\frac{18}{5}$.
• These conversion factors come directly from the definition of the units: 1 km = 1000 m and 1 hour = 3600 s.

Understanding these conversions is crucial for solving problems involving mixed units of distance and time.