Question

A car of mass 1000.0 kg is traveling along a level road at 100.0 km/h when its brakes are applied. Calculate the stopping distance if the coefficient of kinetic friction of the tires is 0.500. Neglect air resistance. (Hint: since the distance traveled is of interest rather than the time, xx is the desired independent variable and not tt. Use the Chain Rule to change the variable: \frac{dv}{dt}=\frac{dv}{dx}\frac{dx}{dt}=v\frac{dv}{dx} ​dt ​ ​dv ​​ = ​dx ​ ​dv ​​ ​dt ​ ​dx ​​ =v ​dx ​ ​dv ​​ .)

Answer 1

To calculate the stopping distance of a car, we can use the equation D = v^2 / (2μg), where D is the stopping distance, v is the initial velocity, μ is the coefficient of kinetic friction, and g is the acceleration due to gravity. Substituting the given values, the stopping distance is approximately 77.1 meters.

Step-by-step explanation:

To calculate the stopping distance of a car, we need to consider the force of friction between the tires and the road. The force of friction can be found using the equation Ff = μN, where Ff is the force of friction, μ is the coefficient of kinetic friction, and N is the normal force acting on the car. The normal force can be calculated as N = mg, where m is the mass of the car and g is the acceleration due to gravity.

Given that the mass of the car is 1000.0 kg, the coefficient of kinetic friction is 0.500, and neglecting air resistance, we can find the force of friction as Ff = (0.500)(1000.0 kg)(9.8 m/s^2).

The stopping distance can be calculated using the equation D = v^2 / (2μg), where D is the stopping distance and v is the initial velocity of the car.

Substituting the values, we can calculate the stopping distance as D = (100 km/h)^2 / (2(0.500)(9.8 m/s^2)).

Converting the velocity to meters per second, we have D = (27.8 m/s)^2 / (9.8 m/s^2).

Therefore, the stopping distance of the car is approximately 77.1 meters.