Below is an explanation of the above listed 1st Distance To Brake To Stop Formula for 5 different Velocities (speeds) between 30km p/h to 80km p/h and from a flat roadway to a 20% descent gradient which are calculated in 5 separate worksheets in Bicycle Brake Stop Calculator  Excel spreadsheet 'StoppingDistance.xls'.  Each of those 5 worksheets also calculate the Distance to Brake to Stop using the above 2nd Distance To Brake To Stop Formula of  .  Significantly, as each of the 5 worksheets show the variance between the calculations of the above described 1st Distance To Brake To Stop Formula and the 2nd Distance To Brake To Stop Formula is less than 1%.

20 km/p/h is 20,000 metres per 3,600 seconds, or 5.556 metres per second.
Assuming a Bicycle Brake Reaction Time of 2.5 seconds, the bicycle will travel 2.5 x  5.556 =  13.89 metres before the brakes are applied, whereupon following the Bicycle Brake Response Time, the bicycle will come to a stop upright.
A Coefficient Of Friction of 0.25 means that the maximum braking force is 25% of the force that the weight of the bicycle exerts onto the road.
On a flat road, the force that the weight of the bicycle plus rider exerts on the road would be the mass of the bike plus rider, times gravity (9.8 metres per second per second).  With a Coefficient Of Friction of 25%, the maximum deceleration would be 25% of 9.8 m/s/s. (Because the maximum braking force depends on the [weight of the bike plus rider] and acts against the [weight of the bike plus rider], the two "weights" cancel out.)
On a 5% ascending slope, a bicycle with a Coefficient Of Friction of 0.25 can decelerate at 30% (0.25 + 5% ascending slope) of 9.8 m/s/s. That is, 2.94 m/s/s. To stop from 5.56 m/s it will take 5.556/2.94 m/p/s - that is, 1.89 seconds.
If the bike starts at 5.556 m/s and decelerates at a constant rate to zero, then its average speed during deceleration is the average of 5.556 and zero. That is, 2.94 m/s.
During 1.89 seconds of deceleration, at an average speed of 2.94 m/s, the bicycle will travel 5.25 metres.
So with a velocity of 20 km/p/h, on a 5% gradient upwards, with a Bicycle Brake Reaction Time of 2.5 seconds, a Bicycle Brake Response Time of 2.27 seconds and a 0.25 Coefficient Of Friction, the shortest possible Distance to Brake to Stop (without skidding) is 13.89 + 5.25 = 19.14 metres during a Time to Brake to Stop of 4.39 seconds. This agrees with Figure 19 above.  It also agrees to 2.08% with the above formula in Figure 19 for km/p/h which calcs 19.54 metres to halt.

20 km/p/h is 20,000 metres per 3,600 seconds, or 5.556 metres per second.
Assuming a Bicycle Brake Reaction Time of 2.5 seconds, the bicycle will travel 2.5 x  5.556 =  13.89 metres before the brakes are applied, whereupon following the Bicycle Brake Response Time, the bicycle will come to a stop upright.
A Coefficient Of Friction of 0.25 means that the maximum braking force is 25% of the force that the weight of the bicycle exerts onto the road.
On a flat road, the force that the weight of the bicycle plus rider exerts on the road would be the mass of the bike plus rider, times gravity (9.8 metres per second per second).  With a Coefficient Of Friction of 25%, the maximum deceleration would be 25% of 9.8 m/s/s. (Because the maximum braking force depends on the [weight of the bike plus rider] and acts against the [weight of the bike plus rider], the two "weights" cancel out.)
On a flat road, a bicycle with a Coefficient Of Friction of 0.25 can decelerate at 25% of 9.8 m/s/s. That is, 2.45 m/s/s. To stop from 5.56 m/s it will take 5.556/2.45 m/p/s - that is, 2.27 seconds.
If the bike starts at 5.556 m/s and decelerates at a constant rate to zero, then its average speed during deceleration is the average of 5.556 and zero. That is, 2.45 m/s.
During 2.27 seconds of deceleration, at an average speed of 5.56 m/s, the bicycle will travel 6.3 metres.
So on a flat road, with a Bicycle Brake Reaction Time of 2.5 seconds, a Bicycle Brake Respo3e Time of 2.27 seconds and a 0.25 Coefficient Of Friction, the shortest possible Distance to Brake to Stop (without skidding) is 13.89 + 6.30 = 20.19 metres during a Time to Brake to Stop of 4.77 seconds. This agrees with Figure 19 above.  It also agrees to 1.97% with the above formula in Figure 19 for km/p/h which calcs 20.58 metres to halt. 

40 km/p/h is 40,000 metres per 3,600 seconds, or 11.11 metres per second.
Assuming a Bicycle Brake Reaction Time of 2.5 seconds, the bicycle will travel 2.5 x  11.11 =  27.78 metres before the brakes are applied, whereupon following the Bicycle Brake Response Time, the bicycle will come to a stop upright.
A Coefficient Of Friction of 0.25 means that the maximum braking force is 25% of the force that the weight of the bicycle exerts onto the road.
On a flat road, the force that the weight of the bicycle plus rider exerts on the road would be the mass of the bike plus rider, times gravity (9.8 metres per second per second). With a Coefficient Of Friction of 25%, the maximum deceleration would be 25% of 9.8 m/s/s. (Because the maximum braking force depends on the [weight of the bike plus rider] and acts against the [weight of the bike plus rider], the two "weights" cancel out.)
On a flat road, a bicycle with a Coefficient Of Friction of 0.25 can decelerate at 25% of 9.8 m/s/s. That is, 2.45 m/s/s. To stop from 11.11 m/s it will take 11.11/2.45 m/p/s - that is, 4.54 seconds.
If the bike starts at 11.111 m/s and decelerates at a constant rate to zero, then its average speed during deceleration is the average of 11.111 and zero. That is, 5.56 m/s.
During 4.54 seconds of deceleration, at an average speed of 2.45 m/s, the bicycle will travel 25.195 metres.
So on a flat road, with a Bicycle Brake Reaction Time of 5.56 seconds, a Bicycle Brake Response Time of 4.54 seconds and a 0.25 Coefficient Of Friction, the shortest possible Distance to Brake to Stop (without skidding) is 27.78 + 25.19 = 52.97 metres during a Time to Brake to Stop of 7.04 seconds. This agrees with Figure 19 above.  It also agrees to 1.5% with the above formula in Figure 19 for km/p/h which calcs 53.77 metres to halt.

30 km/p/h is 30,000 metres per 3,600 seconds, or 8.33 metres per second.
Assuming a Bicycle Brake Reaction Time of 2.5 seconds, the bicycle will travel 2.5 x  8.33 =  20.83 metres before the brakes are applied, whereupon following the Bicycle Brake Response Time, the bicycle will come to a stop upright.
A Coefficient Of Friction of 0.25 means that the maximum braking force is 25% of the force that the weight of the bicycle exerts onto the road.
On a 10% descent slope flat road, the force that the weight of the bicycle plus rider exerts on the road would be the mass of the bike plus rider, times gravity (9.8 metres per second per second). With a Coefficient Of Friction of 25%, the maximum deceleration would be 25% of 9.8 m/s/s. (Because the maximum braking force depends on the [weight of the bike plus rider] and acts against the [weight of the bike plus rider], the two "weights" cancel out.)
On a 10% descending slope, a bicycle with a Coefficient Of Friction of 0.25 can decelerate at 15% (25% less10% slope) of 9.8 m/s/s.  That is, 1.47 m/s/s. To stop from 8.33 m/s it will take 8.33/1.47 m/p/s - that is, 5.67 seconds.
If the bike starts at 8.33 m/s and decelerates at a constant rate to zero, then its average speed during deceleration is the average of 8.33 and zero. That is, 4.167 m/s.
During 5.67 seconds of deceleration, at an average speed of 4.167 m/s, the bicycle will travel 23.62 metres.
So with a velocity of 30 km/p/h, on a 10% gradient downwards, with a Bicycle Brake Reaction Time of 2.5 seconds, a Bicycle Brake Response Time of  5.67 seconds and a 0.25 Coefficient Of Friction, the shortest possible Distance to Brake to Stop (without skidding) is 20.83 + 23.62 = 44.45 metres during a Time to Brake to Stop of 8.17 seconds.  This agrees with Figure 19 above.   It also agrees to 1.34% with the above formula in Figure 19 for km/p/h which calcs 45.05 metres to halt.

50 km/p/h is 50,000 metres per 3,600 seconds, or 13.89 metres per second.
Assuming a Bicycle Brake Reaction Time of 2.5 seconds, the bicycle will travel 2.5 x  13.89 =  34.72 metres before the brakes are applied, whereupon following the Bicycle Brake Response Time, the bicycle will come to a stop upright.
A Coefficient Of Friction of 0.25 means that the maximum braking force is 25% of the force that the weight of the bicycle exerts onto the road.
On a 20% descent slope flat road, the force that the weight of the bicycle plus rider exerts on the road would be the mass of the bike plus rider, times gravity (9.8 metres per second per second).  With a Coefficient Of Friction of 25%, the maximum deceleration would be 25% of 9.8 m/s/s. (Because the maximum braking force depends on the [weight of the bike plus rider] and acts against the [weight of the bike plus rider], the two "weights" cancel out.)
On a 20% descending slope, a bicycle with a Coefficient Of Friction of 0.25 can decelerate at 5% (25% less 20% slope) of 9.8 m/s/s.  That is, 0.49 m/s/s. To stop from 13.89 m/s it will take 13.89/0.49 m/p/s - that is, 28.34 seconds.
If the bike starts at 13.89 m/s and decelerates at a constant rate to zero, then its average speed during deceleration is the average of 13.89 and zero. That is, 6.944 m/s.
During 28.34 seconds of deceleration, at an average speed of 6.944 m/s, the bicycle will travel 196.84 metres.
So with a velocity of 50 km/p/h, on a 20% gradient downwards, with a Bicycle Brake Reaction Time of 2.5 seconds, a Bicycle Brake Response Time of  28.34 seconds and a 0.25 Coefficient Of Friction, the shortest possible Distance to Brake to Stop (without skidding) is 34.72 + 196.84 = 231.56 metres during a Time to Brake to Stop of 30.84 seconds.  This agrees with Figure 19 above.  It also agrees to less than 1% with the above formula in Figure 19 for km/p/h which calcs 232.56 metres to halt.

70 km/h is 70,000 metres per 3,600 seconds, or 19.44 metres per second.
Assuming a Bicycle Brake Reaction Time of 2.5 seconds, the bicycle will travel 2.5 x  19.44 =  48.61 metres before the brakes are applied, whereupon following the Bicycle Brake Response Time, the bicycle will come to a stop upright.
A Coefficient Of Friction of 0.25 means that the maximum braking force is 25% of the force that the weight of the bicycle exerts onto the road.
On a 12% descent slope flat road, the force that the weight of the bicycle plus rider exerts on the road would be the mass of the bike plus rider, times gravity (9.8 metres per second per second). With a Coefficient Of Friction of 25%, the maximum deceleration would be 25% of 9.8 m/s/s. (Because the maximum braking force depends on the [weight of the bike plus rider] and acts against the [weight of the bike plus rider], the two "weights" cancel out.)
On a 12% descending slope, a bicycle with a Coefficient Of Friction of 0.25 can decelerate at 13% (25% less12% slope) of 9.8 m/s/s.  That is, 0.98 m/s/s. To stop from 19.44 m/s it will take 19.44/1.24 seconds - that is, 15.26 seconds.
If the bike starts at 19.44 m/s and decelerates at a constant rate to zero, then its average speed during deceleration is the average of 19.44 and zero. That is, 9.722 m/s.
During 22.68 seconds of deceleration, at an average speed of 11.11 m/s, the bicycle will travel 251.95 metres.
So with a velocity of 70 km/p/h, on a 12% gradient downwards, with a Bicycle Brake Reaction Time of 2.5 seconds, a Bicycle Brake Response Time of 15.26 seconds and a 0.25 Coefficient Of Friction, the shortest possible Distance to Brake to Stop (without skidding) is 48.61 + 148.39 = 197.51 metres during a Time to Brake to Stop of 17.76 seconds.  This is not able to be corroborated with Figure 19 above because that Figure 19 does not calc beyond 50 km/p/h.  However, it agrees to less than 1% with the above formula in Figure 19 for km/p/h which shows calcs 198.39 metres to halt.

80 km/h is 80,000 metres per 3,600 seconds, or 22.22 metres per second.
Assuming a Bicycle Brake Reaction Time of 2.5 seconds, the bicycle will travel 2.5 x  22.22 =  55.56 metres before the brakes are applied, whereupon following the Bicycle Brake Response Time, the bicycle will come to a stop upright.
A Coefficient Of Friction of 0.25 means that the maximum braking force is 25% of the force that the weight of the bicycle exerts onto the road.
On a 15% descent slope flat road, the force that the weight of the bicycle plus rider exerts on the road would be the mass of the bike plus rider, times gravity (9.8 metres per second per second). With a Coefficient Of Friction of 25%, the maximum deceleration would be 25% of 9.8 m/s/s. (Because the maximum braking force depends on the [weight of the bike plus rider] and acts against the [weight of the bike plus rider], the two "weights" cancel out.)
On a 15% descending slope, a bicycle with a Coefficient Of Friction of 0.25 can decelerate at 10% (25% less15% slope) of 9.8 m/s/s.  That is, 0.98 m/s/s. To stop from 22.22 m/s it will take 22.22/0.98 seconds - that is, 22.68 seconds.
If the bike starts at 22.22 m/s and decelerates at a constant rate to zero, then its average speed during deceleration is the average of 22.22 and zero. That is, 11.11 m/s.
During 22.68 seconds of deceleration, at an average speed of 11.11 m/s, the bicycle will travel 251.95 metres.
So with a velocity of 80 km/p/h, on a 15% gradient downwards, with a Bicycle Brake Reaction Time of 2.5 seconds, a Bicycle Brake Response Time of  22.68 seconds and a 0.25 Coefficient Of Friction, the shortest possible Distance to Brake to Stop (without skidding) is 55.56 + 251.95 = 307.51 metres during a Time to Brake to Stop of 25.18 seconds.   This is not able to be corroborated with Figure 19 above because that Figure 19 does not calc beyond 50 km/p/h.  However, it agrees to less than 1% with the above formula in Figure 19 for km/p/h which calcs 309.11 metres to halt.