If the speed of a motor car is doubled , how much more distance will it cover before stopping under the same retarding force ?

Explanation

To solve the problem, we need to understand the relationship between speed, distance, and retarding force. We'll use the work-energy principle, which states that the work done by the retarding force is equal to the change in kinetic energy of the car.

### Step-by-Step Solution:

1. **Define Initial Conditions:**
Let the initial speed of the car be \( v \) and the distance it travels before stopping be \( S \).

2. **Calculate Initial Kinetic Energy:**
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