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  • Calculating Net Force to Stop a Car: A Physics Problem
    Here's how to solve this problem:

    1. Understand the Concepts

    * Newton's Second Law: The net force acting on an object is equal to its mass times its acceleration (F = ma).

    * Constant Acceleration Kinematics: We can use kinematic equations to relate initial velocity (v₀), final velocity (v), acceleration (a), and displacement (Δx).

    2. Determine the Acceleration

    * We know:

    * v₀ = 15.0 m/s (initial velocity)

    * v = 0 m/s (final velocity, the car comes to a halt)

    * Δx = 57.0 m (distance)

    * We need to find 'a' (acceleration).

    We can use the following kinematic equation:

    v² = v₀² + 2aΔx

    * Rearranging to solve for 'a':

    a = (v² - v₀²) / (2Δx)

    * Plugging in the values:

    a = (0² - 15.0²) / (2 * 57.0)

    a ≈ -1.97 m/s² (The acceleration is negative because it's in the opposite direction of the car's motion)

    3. Calculate the Net Force

    * Now we know:

    * m = 1450 kg (mass)

    * a = -1.97 m/s² (acceleration)

    * Using Newton's Second Law (F = ma):

    F = (1450 kg) * (-1.97 m/s²)

    F ≈ -2856.5 N

    Answer:

    The magnitude of the horizontal net force required to bring the car to a halt is approximately 2856.5 N. The negative sign indicates that the force is in the opposite direction of the car's motion.

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