According to the laws of motion, the stopping distance of a car is proportional to the square of its initial velocity. This means that if the car's initial velocity is doubled, its stopping distance will be four times greater.
The skid length is the distance travelled by the vehicle from the instance the brakes are applied till the vehicle stops. Theoretically, the skid length can be calculated using the following formula:
$$Skid Length = {Initial Velocity}^2 / (2 * Coefficient of Friction * Gravitational Acceleration) $$
Where:
- Skid Length: Stopping distance of the car
- Initial Velocity: Initial speed of the car
- Coefficient of Friction: Coefficient of friction between the tire and the road surface
- Gravitational Acceleration: Acceleration due to gravity (approximately 9.81 m/s²)
From this formula, we can see that the skid length is directly proportional to the square of the initial velocity. This means that if the initial velocity is increased, the skid length will increase quadratically.
Therefore, the relationship between skid length and initial velocity is non-linear. The skid length increases more rapidly as the initial velocity increases.
