Understanding the Concepts

* Initial Velocity (v₀): The car's starting speed (19 m/s).

* Final Velocity (v): The car comes to a stop, so its final velocity is 0 m/s.

* Stopping Distance (Δx): The distance the car travels while braking (31 meters).

* Acceleration (a): The rate at which the car slows down (this is what we need to find).

Equation to Use

We can use the following kinematic equation:

v² = v₀² + 2aΔx

Solving for Acceleration

1. Rearrange the equation:

a = (v² - v₀²) / (2Δx)

2. Plug in the values:

a = (0² - 19²) / (2 * 31)

3. Calculate:

a = (-361) / (62)

a ≈ -5.82 m/s²

Important Note: The negative sign indicates that the acceleration is in the opposite direction to the car's initial motion. This means the car is decelerating or slowing down.

Answer: The magnitude of the car's acceleration is approximately 5.82 m/s².