Final answer:
To find the distance a car will skid with locked brakes at a speed of 122.5 km/h, we can use the conservation of energy principle and the formula for kinetic energy. By calculating the initial kinetic energy at 49 km/h and using it to find the distance at 122.5 km/h, we find that the car will skid approximately 306.75 meters.
Step-by-step explanation:
To find the distance a car will skid with locked brakes at a speed of 122.5 km/h, we can use the conservation of energy principle. The energy loss due to sliding friction can be calculated using the initial and final kinetic energies of the car. Since the car skids, its final kinetic energy is zero. Thus, the energy loss is equal to the initial kinetic energy of the car.
Using the formula for kinetic energy: K.E. = 0.5 * m * v^2 (where m is the mass of the car and v is its velocity), we can calculate the initial kinetic energy at 49 km/h and use it to find the distance the car will skid at 122.5 km/h.
Let's calculate it step by step:
- Convert the speeds to meters per second: 49 km/h = 49,000/3.6 m/s = 13,611 m/s and 122.5 km/h = 122,500/3.6 m/s = 33,958.3 m/s
- Calculate the initial kinetic energy at 49 km/h using the formula: K.E. = 0.5 * m * v^2 = 0.5 * m * (13,611^2)
- Calculate the distance the car will skid at 122.5 km/h using the formula: Distance = Energy loss / Sliding friction
By following these steps, we find that the car will skid approximately 306.75 meters with locked brakes at a speed of 122.5 km/h.