Given:
Speed of the car = 25 km/h
Distance to bring the car to rest = 0.5 m

To find:
Distance traveled by the car when running at 75 km/h before coming to rest.

Assumption:
The braking force remains the same for both cases.

Solution:

To solve this problem, we can use the concept of kinetic energy and work done.

1. Calculating Initial Speed:
Given, the speed of the car is 25 km/h. Let's convert it to m/s.
Speed in m/s = (25 km/h) × (1000 m/km) / (3600 s/h) = 6.94 m/s

2. Calculating Initial Kinetic Energy:
The kinetic energy of an object is given by the formula:
Kinetic Energy = 0.5 × mass × velocity^2

Since the mass of the car is not given, we can assume it to be 1 kg for simplicity.
Initial kinetic energy = 0.5 × 1 kg × (6.94 m/s)^2 = 24.04 J

3. Calculating Work Done:
The work done by the braking force to bring the car to rest is equal to the change in kinetic energy.
Work Done = Final Kinetic Energy - Initial Kinetic Energy
Since the car is brought to rest, the final kinetic energy is zero.

Work Done = 0 J - 24.04 J = -24.04 J

4. Calculating Distance Traveled:
The work done by the braking force is given by the formula:
Work Done = Force × Distance

Since the braking force remains the same, we can write:
Force × Distance = -24.04 J

Let's assume the force to be F and the distance traveled to be D.
F × D = -24.04 J

5. Calculating Distance Traveled at 75 km/h:
Given, the speed of the car is 75 km/h. Let's convert it to m/s.
Speed in m/s = (75 km/h) × (1000 m/km) / (3600 s/h) = 20.83 m/s

Using the same braking force, we can write:
F × D' = -24.04 J

Dividing the above two equations, we get:
D' / D = (20.83 m/s) / (6.94 m/s) = 3

Therefore, the distance traveled by the car when running at 75 km/h before coming to rest is 3 times the distance traveled when running at 25 km/h.

Distance traveled at 75 km/h = 3 × 0.5 m = 1.5 m

Answer:
The car will go 1.5 meters before coming to rest when running at 75 km/h, assuming the braking force remains the same.