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.