Question

If v is the initial speed of a vehicle, g is the gravitational acceleration, G is the upward longitudinal slope of the road and fr is the coefficient of rolling friction during braking the braking distance (measured horizontally) for the vehicle to stop is
1. \(\frac{{{\rm{V^2}}}}{{{\rm{g(G +f_r) }}}} \)
2. \(\frac{{{\rm{V^2}}}}{{2{\rm{g(G +f_r) }}}} \)
3. \(\frac{{{\rm{Vg}}}}{{{\rm{(G +f_r) }}}} \)
4. \(\frac{{{\rm{Vf_r}}}}{{{\rm{(G +g) }}}} \)

Answer 1

Correct Answer - Option 2 : \(\frac{{{\rm{V^2}}}}{{2{\rm{g(G +f_r) }}}} \)

Explanation:

Braking distance at downgrade,

\({\left( {{S_b}} \right)_{downgrade}} = \frac{{{V^2}}}{{254\left( {f - G} \right)}}\)

Where V = Design speed in kmph

f = Co-efficient of longitudinal friction, G = Grade

or 

\({\left( {{S_b}} \right)_{downgrade}} = \frac{{{V^2}}}{{2g\left( {f - G} \right)}}\) v in (m/s)

Braking distance at upgrade,

\({\left( {{S_b}} \right)_{upgrade}} = \frac{{{V^2}}}{{254\left( {f + N} \right)}}\)

or 

\({\left( {{S_b}} \right)_{upgrade}} = \frac{{{V^2}}}{{2g\left( {f + G} \right)}}\)  v in (m/s)