Given information:
Speed of the car with brakes applied = 50 km/h
Minimum stopping distance = 6 m

To find:
Minimum stopping distance when the same car is moving at a speed of 100 km/h

Solution:
The stopping distance of a car depends on the speed of the car, the friction between the tires and the road, and the reaction time of the driver.

According to the formula of kinetic energy, the energy possessed by a moving object is given by:

Kinetic energy (K.E.) = 1/2 × mass × velocity^2

When the brakes are applied, the kinetic energy of the car is converted into heat energy due to the friction between the tires and the road. The stopping distance depends on the amount of kinetic energy that needs to be dissipated.

Let's assume the mass of the car to be constant.

When the car is moving at a speed of 50 km/h, its kinetic energy is:

K.E. = 1/2 × mass × (50/3.6)^2 = 347.22 × mass

When the brakes are applied, the kinetic energy of the car is converted into heat energy, which is dissipated by the brakes. This dissipation of energy creates a force that opposes the motion of the car, eventually bringing it to a stop.

The minimum stopping distance for a car moving at a speed of 50 km/h is given as 6 m.

So, the force required to stop the car is:

Force = (mass × velocity^2) / (2 × stopping distance)

= (mass × (50/3.6)^2) / (2 × 6) = 347.22 × mass / 6

Now, when the car is moving at a speed of 100 km/h, its kinetic energy is:

K.E. = 1/2 × mass × (100/3.6)^2 = 1388.89 × mass

The force required to stop the car moving at a speed of 100 km/h is:

Force = (mass × velocity^2) / (2 × stopping distance)

= (mass × (100/3.6)^2) / (2 × stopping distance)

= 4 × (mass × (50/3.6)^2) / (2 × stopping distance)

= 4 × Force

Therefore, the minimum stopping distance for the car moving at 100 km/h is:

Stopping distance = 4 × 6 = 24 m

Hence, the correct answer is option (c) 24 m.

Using v² - u² = 2as