a car is moving at speed of 50km/hr ,can be stopped by brake at least at 6 m.If the same car is moving at speed of 100 km/hr ,what is the minimum stopping distance?

To determine the minimum stopping distance of a car moving at a speed of 100 km/hr, we can use the concept of kinetic energy and the relationship between kinetic energy, mass, and velocity.

The kinetic energy of an object is given by the equation: KE = (1/2) * m * v^2

Where:
- KE represents the kinetic energy
- m represents the mass of the object
- v represents the velocity of the object

Assuming the mass of the car remains constant, the ratio of the kinetic energies can be expressed as:

(KE1 / KE2) = (v1^2 / v2^2)

Given that the car's speed doubles from 50 km/hr to 100 km/hr, the ratio of kinetic energies can be calculated as follows:

(KE1 / KE2) = (50^2 / 100^2) = 0.25

Now, let's calculate the minimum stopping distance at 50 km/hr using the information given. We can solve the equation:

KE = (1/2) * m * v^2

Rearranging the equation to solve for v:

v = √(2 * KE / m)

At 50 km/hr, the velocity can be calculated as follows:

v1 = √(2 * KE1 / m)

Next, let's substitute back into the kinetic energy equation to solve for KE1:

KE1 = (1/2) * m * v1^2

Given that the car can be stopped within 6 meters using the brake, we can set the equation as:

KE1 = (1/2) * m * v1^2 = (1/2) * m * (50 km/hr)^2

Now, let's calculate the minimum stopping distance at 100 km/hr using the calculated ratio of kinetic energies.

KE2 = KE1 * 0.25 = (1/2) * m * (50 km/hr)^2 * 0.25

Finally, we can find the minimum stopping distance at 100 km/hr using the equation for kinetic energy:

d = √(2 * KE2 / m)

Where:
- d represents the stopping distance
- KE2 represents the kinetic energy of the car at 100 km/hr

By plugging in the value of KE2 into the equation, we can calculate the minimum stopping distance at 100 km/hr.

Vf^2-Vi^2=2aS

a=acceleration/deceleration
Vf=final velocity = 0
Vi=initial velocity = 50 or 100
S=distance travelled.
By proportion, double the initial velocity, will quadruple the stopping distance, with the same Vf and a.