At an accident scene on a level road, investigators measure a car's skid mark to be 78 m long.It was a rainy day and the coefficient of friction was estimated to be 0.38. Use these data to determine the speed of the car when the driver slammed on (and locked) the brakes.
40.72 m/s
24.11 m/s
To determine the speed of the car when the driver slammed on the brakes, we can use the concept of kinetic friction. Kinetic friction is the force that opposes the motion of the car as it skids along the road. It can be calculated using the equation:
Frictional force = (coefficient of friction) * (normal force)
The normal force is the force exerted by the road on the car perpendicular to its surface, which is equal to the weight of the car in this case.
The relationship between the frictional force and the kinetic energy of the car can be described using the work-energy principle:
Work done by frictional force = Change in kinetic energy
When the car comes to a stop, its initial kinetic energy will be equal to the work done by the frictional force. The initial kinetic energy of the car is given by:
Initial Kinetic Energy = (1/2) * Mass * (Initial Speed)^2
Since the car's final speed is zero, the change in kinetic energy is equal to the initial kinetic energy.
Putting these equations together, we can solve for the initial speed of the car:
Work done by frictional force = (1/2) * Mass * (Initial Speed)^2
Using the formula for work done by a force (Work = Force * Distance), we can rewrite the equation as:
Force * Distance = (1/2) * Mass * (Initial Speed)^2
Since the force is equivalent to the frictional force and the distance is the length of the skid mark, the equation becomes:
Frictional force * Skid Mark Distance = (1/2) * Mass * (Initial Speed)^2
Now we can substitute the given values into the equation. The skid mark distance is given as 78 m and the coefficient of friction is given as 0.38. We need the mass of the car to complete the calculation, but unfortunately, it is not provided in the question. Without the mass of the car, we cannot determine the initial speed.
To calculate the initial speed, we need the mass of the car.