Question

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 stop) measured along the horizontal (assume all other parameters are kept unchanged)?

• A. $\frac{0.02G}{f_r+0.01G}\times 100$
• B. $\frac{f_r}{f_r+0.02G}\times 100$
• C. $\frac{0.01G}{f_r+0.02G}\times 100$
• D. $\frac{2f_r}{f_r+0.01G}\times 100$

Answer 1

The correct option is C $\frac{0.01G}{f_r+0.02G}\times 100$

Case I: Braking distance
$=\frac{v^2}{2g(f_r+0.01G)}$

Case II: Braking distance
$=\frac{v^2}{2g(f_r+0.02G)}$

Percentage change
$=\frac{\frac{v^2}{2g(f_r+0.01G)}-\frac{v^2}{2g(f_r+0.02G)}}{\frac{v^2}{2g(f_r+0.01G)}}\times 100$

$=\frac{0.01G}{(f_r+0.02G)}\times 100$