Question

A car is traveling at 56.9 km/h on a flat highway. the acceleration of gravity is 9.8 m/s 2 . if the coefficient of friction between the road and the tires on a rainy day is 0.109, what is the minimum distance in which the car will stop?

Answer 1

`Given:\\v=56.9 (km)/(h) \approx 15.81 (m)/(s) \\g=9.8 (m)/(s^2) \\\mu=0.109\\\\Find:\\s=?\\\\Solution:\\\\s=vt- (at^2)/(2) \\\\a= (v)/(t) \Rightarrow t= (v)/(a) \\\\s= (v^2)/(a) - (v^2)/(2a) =(v^2)/(2a) \\\\a= (F)/(m) \\\\F=T=\mu N\\\\N=mg\\\\F=\mu mg\\\\a= (\mu mg)/(m) =\mu g\\\\s= (v^2)/(2\mu g) \\\\\\s= ((15.81 (m)/(s))^2)/(2\cdot 0.109\cdot9.8 (m)/(s^2) ) \approx 117m`