The coefficient of average rolling friction of a road is fr and its grade is +G%. If the grade of this road is doubled, what will be the percentage change in the braking distance

Q. The coefficient of average rolling friction of a road is f_r and its grade is +G%. If the grade of this road is doubled, what will be the percentage change in the braking distance (for the design vehicle to come to a stop) measured along the horizontal (assume all other parameters are kept unchanged)?

Ans:

Solution:

Braking distance is the distance traveled by the vehicle from the moment when the brake was applied to the moment when the vehicle stops.  Braking distance is also the work done by the frictional force on to the vehicle to stop it completely.

Where V = Speed of the vehicle before the brake is applied                 

 f = coefficient of lateral friction                 

 G = gradient in percentage                

  η = braking efficiency