Answer :
To determine how far the car will skid at 140 km/h given a skid distance at 40 km/h, we use the work-energy principle and consider the quadratic relationship between speed and stopping distance due to friction, leading to a calculation that shows the skid distance will increase with the square of the speed increase.
The stopping distance is related to the square of the initial velocity, because kinetic energy, which is proportional to the square of the velocity, must be dissipated through friction to stop the car.
Using the work-energy principle, the work done by friction to stop the car is equal to the initial kinetic energy of the car. Since the coefficient of friction and the mass of the car are constant, the skid distance is proportional to the square of the initial speed.
If the car skids 16 m at 40 km/h, to find the skid distance at 140 km/h, we can set up a proportion because the relationship is quadratic: (140/40)^2 = (skid distance at 140 km/h) / 16 m. Solving for the skid distance at 140 km/h gives a significantly larger distance due to the increase in speed.
