A vacant, 1560 kg car begins from rest and rolls 46 meters down an inclined plateau before rolling off the edge and crashing into the sea below. The plateau is at a constant downward angle of 12.4 degrees with the horizontal. The coefficient of rolling friction between the car and the plateau is 0.125 and the edge of the plateau is 55 meters above the sea.

At what rate was the car accelerating as it rolled down the plateau?

This is one of those problems where you have to weed out or ignore the information you don't need.

The component of the weight force along the incline is M g sin 12.4. Opposed to that is the rolling friction, which is M g cos 12.4 * 0.125. Subtract the second number from the first for the net force that causes acceleration. Then divide by the mass M for the acceleration, a. Since mass cancels out,
a = g (sin 12.4 - 0.125 cos 12.4)

To find the rate at which the car was accelerating as it rolled down the plateau, we can use the principles of physics, specifically the concept of forces and their effects on motion.

First, we need to analyze the forces acting on the car. The main forces at play here are the gravitational force and the force of rolling friction. The gravitational force is acting vertically downward and can be resolved into two components: a component parallel to the inclined plateau (the driving force) and a component perpendicular to the plateau (the normal force).

The driving force component is given by the equation:
Driving Force = m * g * sin(θ)
where:
- m is the mass of the car (1560 kg)
- g is the acceleration due to gravity (9.8 m/s^2)
- θ is the angle of the plateau (12.4 degrees)

The force of rolling friction acts in the opposite direction to the motion and is given by:
Friction Force = μ * m * g * cos(θ)
where:
- μ is the coefficient of rolling friction (0.125)

At the start when the car is at rest, the driving force is equal to the friction force. Therefore, we have the equation:
m * g * sin(θ) = μ * m * g * cos(θ)

Next, we need to determine the acceleration of the car. The net force acting on the car is equal to the driving force minus the friction force, so:
Net Force = Driving Force - Friction Force
Using Newton's second law of motion (F = ma), we have:
m * a = m * g * sin(θ) - μ * m * g * cos(θ)
Canceling out the mass of the car on both sides of the equation, we are left with:
a = g * sin(θ) - μ * g * cos(θ)

Now, we can substitute the given values into the equation to get the acceleration:
a = (9.8 m/s^2) * sin(12.4 degrees) - (0.125) * (9.8 m/s^2) * cos(12.4 degrees)
a ≈ 1.687 m/s^2

Therefore, the car was accelerating at a rate of approximately 1.687 m/s^2 as it rolled down the plateau.