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, x is the desired independent variable and not t. Use the Chain Rule to change the variable: dv/dx= dv/dx. dx/dt=vdv/dx

a) 500 m
b) 750 m
c) 1000 m
d) 1250 m

Answer 1

To calculate the stopping distance of a car when its brakes are applied, we can use the equation: d = v^2 / (2a), where d is the stopping distance, v is the initial velocity, and a is the acceleration. In this case, the stopping distance of the car is approximately 265.1 m.

Step-by-step explanation:

To calculate the stopping distance of a car when its brakes are applied, we can use the equation:

d = v2 / (2a)

Where d is the stopping distance, v is the initial velocity, and a is the acceleration.

In this case, the initial velocity is 100.0 km/h, which can be converted to m/s (27.8 m/s), and the acceleration is given by the equation:

a = μg

Where μ is the coefficient of kinetic friction and g is the acceleration due to gravity. Plugging in the values, we get:

a = (0.500)(9.8 m/s2) = 4.9 m/s2

Substituting into the first equation, we get:

d = (27.8 m/s)2 / (2(4.9 m/s2)) = 265.1 m

Therefore, the stopping distance of the car is approximately 265.1 m.