Answer :
The force of friction between the car's tires and the pavement can be calculated using the equation:
Force of friction = mass x acceleration
First, let's calculate the acceleration of the car. We can use the formula:
Final velocity^2 = Initial velocity^2 + 2 x acceleration x distance
Since the car comes to a stop, the final velocity is 0 m/s. The initial velocity is 14 m/s, and the distance is 106 m. Substituting these values into the equation, we get:
0^2 = 14^2 + 2 x acceleration x 106
Simplifying the equation, we have:
0 = 196 + 212 x acceleration
Rearranging the equation, we find:
Acceleration = -196 / (212)
Acceleration ≈ -0.925 m/s^2
Since the car is slowing down, the acceleration is negative.
Now, we can calculate the force of friction using the equation:
Force of friction = mass x acceleration
The mass of the car is given as 2,165 kg, and the acceleration is -0.925 m/s^2. Substituting these values into the equation, we get:
Force of friction = 2,165 kg x (-0.925 m/s^2)
Force of friction ≈ -2,000.125 N
Since force is a vector quantity, the negative sign indicates that the force of friction acts in the opposite direction to the car's motion. However, in this context, we can consider the magnitude of the force, which is approximately 2,000.125 N.
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