Understanding Speed, Distance, and Time Calculation

This problem involves calculating the time taken to cover a certain distance when the speed is known. We are given the speed of Sonu's car and the total distance to be covered. The key is to ensure that the units of speed, distance, and time are consistent before applying the formula.

Given Information

• Speed of the car = 20 m/s
• Distance to be covered = 936 km

Finding the Time Taken

The fundamental relationship between speed, distance, and time is:

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

However, the given speed is in meters per second (m/s), and the distance is in kilometers (km). The options for time are in hours (hr). To calculate the time in hours, we need to convert the units so they are consistent, preferably kilometers per hour (km/hr) for speed and kilometers (km) for distance, or meters (m) for distance and meters per second (m/s) for speed, and then convert the time to hours.

Converting Speed from m/s to km/hr

To convert speed from meters per second (m/s) to kilometers per hour (km/hr), we use the conversion factor:

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

So, 1 m/s can be written as:

$$ 1 \text{ m/s} = \frac{1 \text{ m}}{1 \text{ s}} = \frac{\frac{1}{1000} \text{ km}}{\frac{1}{3600} \text{ hr}} = \frac{1}{1000} \times \frac{3600}{1} \text{ km/hr} = \frac{3600}{1000} \text{ km/hr} = \frac{18}{5} \text{ km/hr} $$

Alternatively, to convert m/s to km/hr, multiply by $\frac{18}{5}$. To convert km/hr to m/s, multiply by $\frac{5}{18}$.

Now, let's convert the speed of 20 m/s to km/hr:

$$ \text{Speed} = 20 \text{ m/s} = 20 \times \frac{18}{5} \text{ km/hr} $$

$$ \text{Speed} = 4 \times 18 \text{ km/hr} $$

$$ \text{Speed} = 72 \text{ km/hr} $$

So, Sonu is driving at a speed of 72 km/hr.

Calculating Time Taken in Hours

Now we have the distance in km and the speed in km/hr. We can use the formula:

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

Substitute the values:

$$ \text{Time} = \frac{936 \text{ km}}{72 \text{ km/hr}} $$

Let's perform the division:

$$ \text{Time} = \frac{936}{72} \text{ hours} $$

We can simplify the fraction by dividing both numerator and denominator by common factors. Both are divisible by 2, 4, 8, and 9.

Divide by 8: $936 \div 8 = 117$, $72 \div 8 = 9$.

So, the fraction becomes $\frac{117}{9}$.

Now, divide 117 by 9:

$$ 117 \div 9 = 13 $$

Therefore, the time taken is 13 hours.

Result

Sonu will cover a distance of 936 km in 13 hours at a speed of 20 m/s (or 72 km/hr).

Checking Options

Let's compare our calculated time with the given options:

Our calculated time of 13 hours matches Option 4.

Revision Table: Speed, Distance, Time Formula

Additional Information: Unit Conversion Tips

Converting between different units of speed, distance, and time is a common task in physics and everyday calculations. Here are some key conversions:

• Distance: 1 km = 1000 m, 1 m = 100 cm
• Time: 1 hour = 60 minutes, 1 minute = 60 seconds, 1 hour = 3600 seconds
• Speed (m/s to km/hr): Multiply by $\frac{18}{5}$
• Speed (km/hr to m/s): Multiply by $\frac{5}{18}$

Always check the units of the given values and the required units for the answer to ensure you perform the correct conversions before using the formulas.