Two cars are travelling towards each other with speed of 45 km/hr and 63km/hr respectively. What is the distance (in kilometres) between the two cars ten second before they collide?

Options

A. `0.5`
B. `0.2`
C. `0.3`
D. `0.45`

Answer

To find the distance between the two cars ten seconds before they collide, we can follow these steps:

### Step 1: Calculate the relative speed of the two cars.
The two cars are traveling towards each other, so we can add their speeds to find the relative speed.

- Speed of Car A = 45 km/hr
- Speed of Car B = 63 km/hr

**Relative Speed = Speed of Car A + Speed of Car B**
\[ \text{Relative Speed} = 45 \text{ km/hr} + 63 \text{ km/hr} = 108 \text{ km/hr} \]

### Step 2: Convert the relative speed from km/hr to m/s.
To convert km/hr to m/s, we can use the conversion factor \( \frac{5}{18} \).

\[ \text{Relative Speed in m/s} = 108 \text{ km/hr} \times \frac{5}{18} = 30 \text{ m/s} \]

### Step 3: Calculate the distance covered by the cars in 10 seconds.
Using the formula:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
we can find the distance covered by both cars in 10 seconds.

\[ \text{Distance in 10 seconds} = 30 \text{ m/s} \times 10 \text{ s} = 300 \text{ m} \]

### Step 4: Convert the distance from meters to kilometers.
Since 1 km = 1000 m, we can convert the distance:

\[ \text{Distance in km} = \frac{300 \text{ m}}{1000} = 0.3 \text{ km} \]

### Step 5: Find the distance between the two cars ten seconds before they collide.
The distance between the two cars ten seconds before they collide is the distance they would cover in that time, which we calculated as 0.3 km.

Thus, the distance between the two cars ten seconds before they collide is **0.3 km**.

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