calculate the skid-to- stop distance of a car traveling on a road at 100km h with a coefficient of friction of 0.68
To calculate the skid-to-stop distance of a car, you can use the following formula:
Skid-to-Stop Distance = (Initial Velocity^2) / (2 * Acceleration)
In this case, we need to convert the initial velocity from km/h to m/s, as the formula requires velocity in meters per second.
Step 1: Convert the Initial Velocity from km/h to m/s
Initial Velocity = 100 km/h
To convert km/h to m/s, divide the velocity by 3.6:
Initial Velocity = 100 km/h = (100/3.6) m/s ≈ 27.8 m/s
Step 2: Calculate the Acceleration
Frictional Force = Coefficient of Friction * Normal Force
The normal force is the force exerted by the car's weight on the road surface. It is equal to the car's mass (m) multiplied by the acceleration due to gravity (g). In this case, we'll assume m = 1000 kg.
Acceleration = Frictional Force / Mass
To find the frictional force, multiply the coefficient of friction by the normal force:
Frictional Force = Coefficient of Friction * (m * g)
The acceleration due to gravity (g) is approximately 9.8 m/s^2.
Acceleration = (Coefficient of Friction * m * g) / m
Acceleration = Coefficient of Friction * g ≈ 0.68 * 9.8 ≈ 6.7 m/s^2
Step 3: Evaluate the Formula
Skid-to-Stop Distance = (Initial Velocity^2) / (2 * Acceleration)
Skid-to-Stop Distance = (27.8^2) / (2 * 6.7) ≈ 117.7 meters
Therefore, the skid-to-stop distance of the car traveling at 100 km/h with a coefficient of friction of 0.68 is approximately 117.7 meters.