A 1340 kg car is traveling with a speed of 15.0 m/s. What is the magnitude of the horizontal net force that is required to bring the car to a halt in a distance of 51.5 m?

To find the magnitude of the horizontal net force required to bring the car to a halt, we can use Newton's second law of motion, which states that the net force acting on an object is equal to its mass multiplied by its acceleration.

First, we need to find the acceleration of the car. We can use the kinematic equation:

v^2 = u^2 + 2as

where v is the final velocity (0 m/s), u is the initial velocity (15.0 m/s), a is the acceleration, and s is the distance traveled (51.5 m).

Rearranging the equation to solve for acceleration, we have:

a = (v^2 - u^2) / (2s)

Substituting the values into the equation:

a = (0^2 - 15.0^2) / (2 * 51.5)

a = (-225.0) / 103

a ≈ -2.18 m/s^2

Note: The negative sign indicates that the acceleration is in the opposite direction of the car's initial velocity.

Now that we have the acceleration, we can find the magnitude of the net force by multiplying the mass of the car (1340 kg) by the acceleration (-2.18 m/s^2):

net force = mass x acceleration

net force = 1340 kg x (-2.18 m/s^2)

net force ≈ -2909.2 N

Since force is a vector quantity, the magnitude of the net force is always positive. Therefore, the magnitude of the horizontal net force required to bring the car to a halt is approximately 2909.2 Newtons.