This question is typical on some driver's license exams: A car moving at 50km/hr skids 15m with locked brakes.How far will the car skid with locked brakes at 120 km/h?

A cars kinetic energy is proportional to the square of it's speed. The energy dispensed in braking is proportional to the braking distance.

Therefore the braking distance is proportional to the square of the speed, as in (120 km/hr / 50 km/hr)² * 15m

To find the distance the car will skid with locked brakes at 120 km/h, we can use the concept of ratio and proportion.

Let's set up a proportion using the information given:

50 km/h corresponds to 15 m of skid distance.

120 km/h corresponds to 'x' meters of skid distance.

The proportion can be set up as follows:

(50 km/h) / (15 m) = (120 km/h) / (x m)

Now we can cross-multiply and solve for 'x':

(50 km/h) * (x m) = (120 km/h) * (15 m)

50x = 120 * 15

Now, divide both sides of the equation by 50 to solve for 'x':

x = (120 * 15) / 50

Calculating this value, we get:

x = 36

Therefore, the car will skid approximately 36 meters with locked brakes at 120 km/h.

To answer this question, we need to understand the relationship between the speed of a car and the distance it skids with locked brakes. This relationship is often referred to as the "stopping distance."

The stopping distance of a car depends on two factors: the initial velocity (speed) of the car and the coefficient of friction between the car's tires and the road.

The coefficient of friction represents the grip or traction between the tires and the road surface. It affects how quickly the car can decelerate or come to a stop. In this case, we assume that the coefficient of friction remains constant throughout the calculation.

Typically, the stopping distance is directly proportional to the square of the initial velocity. This means that if the speed doubles, the stopping distance quadruples.

Now, let's calculate the stopping distance at 120 km/h using the information given.

First, we need to convert the speeds to m/s since the units in the question are in meters. We know that 1 km/h is equal to 0.2778 m/s.

Speed at 50 km/h = 50 km/h * 0.2778 m/s = 13.89 m/s
Speed at 120 km/h = 120 km/h * 0.2778 m/s = 33.33 m/s

Next, we can use the formula for the stopping distance:

Stopping distance = (initial velocity^2) / (2 * coefficient of friction * acceleration due to gravity)

Since we are comparing two scenarios, we can set up a ratio:

50^2 / 120^2 = Stopping distance at 50 km/h / Stopping distance at 120 km/h

Cross-multiplying, we have:

Stopping distance at 120 km/h = (120^2 * Stopping distance at 50 km/h) / 50^2

Plugging in the values:

Stopping distance at 120 km/h = (14400 * 15) / 2500 = 86.4 m

Therefore, the car will skid approximately 86.4 meters with locked brakes at 120 km/h.