Two cars are travelling towards each other at speed of $$20 \text{ m s}^{-1}$$ each. When the cars are $$300 \text{ m}$$ apart, both the drivers apply brakes and the cars retard at the rate of $$2 \text{ m s}^{-2}$$. The distance between them when they come to rest is :

Two cars travel towards each other at 20 m/s each, initially 300 m apart, both braking with retardation 2 m/s$$^2$$. We need the distance between them when they stop.

Using the kinematic equation $$v^2 = u^2 - 2as$$ (where $$v = 0$$ at stop):

$$ 0 = (20)^2 - 2(2)s $$

$$ 0 = 400 - 4s $$

$$ s = \frac{400}{4} = 100 \text{ m} $$

Each car travels 100 m before stopping.

Both cars move toward each other, so the total distance closed between them is:

$$ s_{total} = 100 + 100 = 200 \text{ m} $$

Initial separation was 300 m. After both cars stop:

$$ d = 300 - 200 = 100 \text{ m} $$

The distance between them when they come to rest is 100 m.

The correct answer is Option (2): 100 m.