On fogy day two drivers spot in front of each other when 80 m apart, they were travelling 70 kmph and 60 kmph. Both apply brakes simultaneously which retards the car at the rate of `5 m//s^2`. Which of the following statement is correct?

Options

A. The collision will be averted
B. The collision will takes place
C. They will cross each other
D. They will just collide

Answer

To solve the problem, we need to determine whether the two cars will collide or not after applying brakes. Here’s a step-by-step solution:

### Step 1: Convert speeds from km/h to m/s
- For Car 1 (speed = 70 km/h):
\[ u_1 = 70 \times \frac{5}{18} = \frac{350}{18} \approx 19.44 \text{ m/s} \]

- For Car 2 (speed = 60 km/h):
\[ u_2 = 60 \times \frac{5}{18} = \frac{300}{18} \approx 16.67 \text{ m/s} \]

### Step 2: Calculate stopping distance for Car 1
Using the formula \( v^2 = u^2 + 2as \), where:
- \( v = 0 \) (final velocity when the car stops)
- \( u = 19.44 \text{ m/s} \)
- \( a = -5 \text{ m/s}^2 \)

Substituting the values:
\[ 0 = (19.44)^2 + 2 \times (-5) \times s_1 \]
\[ 0 = 377.7936 - 10s_1 \]
\[ 10s_1 = 377.7936 \]
\[ s_1 = \frac{377.7936}{10} \approx 37.78 \text{ m} \]

### Step 3: Calculate stopping distance for Car 2
Using the same formula:
- \( v = 0 \) (final velocity when the car stops)
- \( u = 16.67 \text{ m/s} \)
- \( a = -5 \text{ m/s}^2 \)

Substituting the values:
\[ 0 = (16.67)^2 + 2 \times (-5) \times s_2 \]
\[ 0 = 277.6889 - 10s_2 \]
\[ 10s_2 = 277.6889 \]
\[ s_2 = \frac{277.6889}{10} \approx 27.77 \text{ m} \]

### Step 4: Calculate total distance traveled before stopping
Now, we need to find the total distance traveled by both cars before they stop:
\[ \text{Total distance} = s_1 + s_2 = 37.78 \text{ m} + 27.77 \text{ m} \approx 65.55 \text{ m} \]

### Step 5: Compare total distance with initial distance
The initial distance between the two cars is 80 m. Since the total distance traveled by both cars before stopping (65.55 m) is less than the initial distance (80 m), they will not collide.

### Conclusion
The correct statement is: **The collision will be averted.**

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