91Ó°ÊÓ

Frictional force is a crucial player in understanding car skidding. It refers to the force resisting the relative motion of a sliding object on a surface. In this context, the frictional force acts between the car's tires and the road as the car tries to stop.

There are different types of friction, but here we focus on kinetic friction because the car's wheels are locked and skidding across the pavement. The kinetic friction is what slows the car down, acting as a force opposite to the car's initial motion.

It’s determined by the formula: \[F_{\text{friction}} = \mu_k \times m \times g, \]where

• \(F_{\text{friction}}\) is the frictional force,
• \(\mu_k\) is the coefficient of kinetic friction,
• \(m\) is the mass of the car, and
• \(g\) is the acceleration due to gravity.

The frictional force is what causes the car to decelerate and eventually stop. Understanding this helps in determining whether a car was speeding by analyzing the length of the skid marks.

The coefficient of kinetic friction, denoted as \(\mu_k\), characterizes how much frictional force exists between the two surfaces in contact during motion. It is a dimensionless quantity representing the ratio between the force of kinetic friction and the normal force acting on the object.

In our case, \(\mu_k = 0.750\) suggests relatively high friction between the road and the car's tires. It implies that the road and tires form a surface interaction that effectively slows down the car once the brakes are applied and the tires locked.

To determine the car's speed when it started skidding, the coefficient helps calculate the frictional force as \[a = \mu_k \times g\]where:

• \(a\) is the acceleration (or deceleration in this scenario).

Knowing \(\mu_k\) leads to finding the deceleration, a critical step in checking how fast the vehicle was traveling initially.

Constant acceleration means that the rate of change of velocity remains the same over time. In this scenario, the term is part of the narrative because when the car's brakes are applied, it experiences a steady deceleration.

Understanding constant acceleration is fundamental in using kinematic equations to solve motion problems. The crucial equation in this context is: \[v^2 = u^2 + 2as,\]where:

• \(v\) is the final velocity (0 ft/s here because the car stops),
• \(u\) is the initial velocity,
• \(a\) is the constant acceleration (negative because it's deceleration), and
• \(s\) is the displacement (192 ft in this case).

This equation allows us to discover how fast the car was going before it began stopping. With constant acceleration, calculations become straightforward as the equations do not change their form, simplifying the computational process within physics problems.