Final answer:
By applying the work-energy principle and using the coefficient of kinetic friction, skid distance, and the acceleration due to gravity, the initial velocity of a car that left 95.0-meter-long skid marks can be calculated. The result is approximately 30.2 m/s, which does not match the provided answer choices; hence, data or choices should be reviewed for accuracy.
Step-by-step explanation:
To determine how fast the car was moving when the driver hit the brakes with 95.0-meter-long skid marks and a coefficient of kinetic friction of 0.460, we can use the formula for kinetic energy and the work-energy principle. The work done by friction is equal to the kinetic energy of the car just before the driver initiated the brakes.
The formula to calculate the initial velocity (v) is obtained after equating the work done by friction (Work = Friction Force × Distance) to the initial kinetic energy of the car (KE = 1/2 mv²). We know the work done by friction is equal to the kinetic energy because the car comes to a complete stop.
Work = Friction Force × Distance = (Coefficient of Friction) × (Weight of the Car) × (Skid Distance) = (Kinetic Energy) = 1/2 m v²
Since the weight of the car is the mass (m) times the acceleration due to gravity (g), we can rewrite this as:
Work = (Friction Coefficient) × m × g × Distance = 1/2 m v²
Canceling the mass from both sides and solving for 'v' gives us:
v = sqrt(2 × Friction Coefficient × g × Distance)
Plugging in the values, v = sqrt(2 × 0.460 × 9.81 m/s² × 95.0 m), we find that v ≈ 30.2 m/s. This answer is not one of the options provided, so there may be either a typo in the options or an error in the given data. It's crucial to double-check the options and the given data to ensure the correct answer.