Question

If a motor cyclist covers a distance of 1200 m in 2 min 30 sec., then the speed (in km/hr) of the cyclist is :

• A. $12\frac{1}{2}$
• B. $28\frac{4}{5}$
• C. 25
• D. 28

Hint:

To convert speed quickly between units:
- Multiply by $\frac{18}{5}$ to convert $\text{m/s} \rightarrow \text{km/hr}$.
- Multiply by $\frac{5}{18}$ to convert $\text{km/hr} \rightarrow \text{m/s}$.
Keep these ratios handy to solve speed problems rapidly.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
This question belongs to the topic of Speed, Time, and Distance.
The basic physical relation defines speed as the distance covered per unit of time.
Here, the distance is provided in meters and the time is given in minutes and seconds.
We need to calculate the speed of the cyclist and convert the unit from meters per second ($\text{m/s}$) to kilometers per hour ($\text{km/hr}$).

Step 2: Key Formula or Approach:
The basic formula for speed ($v$) is:
\[ v = \frac{\text{Distance } (D)}{\text{Time } (T)} \] To convert speed from $\text{m/s}$ to $\text{km/hr}$, we multiply the value by $\frac{18}{5}$ because:
\[ 1 \text{ m/s} = \frac{\frac{1}{1000} \text{ km}}{\frac{1}{3600} \text{ hr}} = \frac{3600}{1000} \text{ km/hr} = \frac{18}{5} \text{ km/hr} \]

Step 3: Detailed Explanation:

• Convert Time into Seconds:
The given time is $2 \text{ minutes and } 30 \text{ seconds}$.
Since $1 \text{ minute} = 60 \text{ seconds}$:
\[ T = (2 \times 60) + 30 = 120 + 30 = 150 \text{ seconds} \]

• Calculate Speed in m/s:
The distance covered is $D = 1200 \text{ m}$.
Using the speed formula:
\[ v = \frac{1200}{150} = 8 \text{ m/s} \]

• Convert Speed to km/hr:
Multiply the speed in $\text{m/s}$ by $\frac{18}{5}$:
\[ v = 8 \times \frac{18}{5} = \frac{144}{5} \text{ km/hr} \]

• Express as a Mixed Fraction:
Divide $144$ by $5$:
\[ 144 = 28 \times 5 + 4 \]
Therefore:
\[ v = 28\frac{4}{5} \text{ km/hr} \]

Step 4: Final Answer:
The speed of the motorcyclist is $28\frac{4}{5} \text{ km/hr}$.
Hence, the correct option is (B).