**The Correlation Between Speed and Distance After Applying Brakes**

The correlation between the speed of an automobile and the distance it travels after applying the brakes can be characterized as **positive**. This means that as the speed of the automobile increases, the distance it travels after applying the brakes also increases.

**Explanation:**

1. **Physics of Braking:** To understand the correlation, it is important to consider the physics behind braking. When a driver applies the brakes, the frictional force between the tires and the road surface opposes the forward motion of the vehicle, causing it to decelerate. This force is directly proportional to the weight of the vehicle and the coefficient of friction between the tires and the road.

2. **Braking Distance:** The braking distance refers to the distance a vehicle travels from the moment the brakes are applied until it comes to a complete stop. It is influenced by various factors such as the initial speed of the vehicle, the efficiency of the braking system, the condition of the tires, and the road surface.

3. **Influence of Speed on Braking Distance:** The speed of the automobile has a significant impact on the braking distance. According to the laws of physics, the kinetic energy of a moving object is proportional to the square of its velocity. Therefore, if the speed of the automobile doubles, its kinetic energy will increase four times.

4. **Braking Force vs. Kinetic Energy:** The braking force generated by the friction between the tires and the road is limited. As the speed of the automobile increases, the kinetic energy also increases, requiring a larger braking force to bring the vehicle to a stop within a certain distance.

5. **Increased Braking Distance:** Due to the limitations of the braking force, a higher initial speed results in a longer braking distance. The vehicle takes more time to decelerate and stop, covering a greater distance during that time. Therefore, the correlation between speed and distance after applying the brakes is positive.

Overall, it is important for drivers to understand the relationship between speed and braking distance to ensure safe driving. Higher speeds require longer braking distances, and maintaining an appropriate speed can help reduce the risks of accidents and collisions.

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