Physics

1. Given:

Mass ratio:

Kinetic energy ratio:

The coefficient of friction between the cars and the road is the same for both cars.

 

2. Relation Between Kinetic Energy and Stopping Distance:

The work done by the frictional force to stop the car is equal to the change in kinetic energy:

 

The work done by the friction force (where is the coefficient of friction and is the acceleration due to gravity), is equal to the kinetic energy lost as the car stops. The stopping distance is related to the kinetic energy and friction force by:

 

Therefore, the stopping distance for a car is:

 

Since both cars experience the same frictional force per unit mass, we can use this equation to find the ratio of stopping distances.

 

3. Calculating the Stopping Distance:

The kinetic energy for each car is:

For car A:

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