Final answer:
To find out how far the car would skid at 144 km/h, we use the conservation of energy and the fact that kinetic energy is proportional to the square of the velocity. Since the velocity is three times greater, the skid distance will be nine times longer, resulting in a skid distance of approximately 144 meters.
Step-by-step explanation:
The question is asking to determine how far a car will skid with locked brakes at a higher speed, given that it skids a certain distance at a lower speed. We can assume that the energy loss due to sliding friction is the same, which means we are dealing with the concept of conservation of energy.
When a car with locked brakes skids to a stop, all of its initial kinetic energy is converted into heat and sound due to friction. The work done by friction is equal to the initial kinetic energy. Since work is defined by the product of the force (friction in this case) and distance, we can express it as Work = Force × Distance = Kinetic Energy. Assuming the coefficient of friction is the same for both speeds, we can use the formula: KE = ½ × m × v² (where m is mass and v is velocity) to find the distance the car will skid at the higher speed.
Taking the distances at the given speeds, we can set up a ratio because kinetic energy is proportional to the square of the velocity. The initial skid distance at 48 km/h (which we convert to 13.3 m/s) is 16 meters. Since the velocity at 144 km/h (which is 40 m/s) is three times that at 48 km/h, we square this ratio (3² = 9) to get the proportionality for the skid distance at the higher speed. Multiplying the initial skid distance by this ratio gives us: 16 m × 9 = 144 m. Therefore, at 144 km/h, the car will skid approximately 144 meters.