Final answer:
The correct answer is option B, which states that the magnitude of the force is 14157.22 N directed backward, and the force was provided by friction between the tires and the road. This is calculated based on the work-energy principle, considering the change in kinetic energy and the distance over which the car stops.
Step-by-step explanation:
The magnitude and direction of the force that acted on a car with a mass of 1225 kg when it slows to a stop can be calculated using the work-energy principle, which states that the work done by the net force acting on an object results in a change in the object's kinetic energy. We can find the work done, and then using this to calculate the force.
To calculate the work done on the car (W), we use the equation W = ∆K.E., where ∆K.E. (change in kinetic energy) is equal to the final kinetic energy (½mv²) minus the initial kinetic energy (½mv²). Since the car stops, the final kinetic energy is 0, and the initial kinetic energy can be calculated using the given mass (m = 1225 kg) and initial velocity (v = 35 m/s). This gives us:
Initial K.E. = ½ * 1225 kg * (35 m/s)² = 750,312.5 Joules
Since the car is coming to a stop, the work done (which is equal to the change in kinetic energy) is:
W = 0 - 750,312.5 Joules = -750,312.5 Joules
To find the magnitude of the net force (F), we use the work = force × distance equation where the work done is -750,312.5 Joules and the distance (d) is 53 meters. We therefore have force (F) multiplied by distance (d) equal to the work done:
F * 53 m = -750,312.5 Joules
So, F = -750,312.5 Joules / 53 m = -14157.22 N
The negative sign indicates that the force acts opposite to the direction of motion which is backward relative to the car's initial motion; this would be the force of friction between the tires and the road which acts to stop the car. Therefore, the correct description would be:
B) The magnitude of the force is 14157.22 N directed backward, and the force was provided by friction between the tires and the road.