Bicycle Braking: Dry vs Wet Asphalt at 15 m
At a school cycling safety session, a student tests braking on a flat asphalt court. The bicycle and rider have a combined mass of 80 kg and travel at 8.0 m/s. The student's reaction time is 0.80 s. On dry asphalt the brakes produce a deceleration of 4.0 m/s²; on wet asphalt the deceleration is 2.5 m/s². A marker is placed 15 m ahead to represent a car pulling out. The student first tests on dry asphalt, then on wet asphalt. The bike's tyres are smooth in the centre. The student wants to know whether speed or road condition matters more, and what the 15 m marker shows about safety. Ignore air resistance. The court is level, and the student keeps the same riding position in both tests.
1. Calculate the total stopping distance on dry and wet asphalt. Show the reaction distance and braking distance separately.
Read the worked answer
- Reaction distance = (v\times t=8.0\times0.80=6.4\text{ m}).
- Braking distance = (v^2/(2a)).
- Dry asphalt:
(8.0^2/(2\times4.0)=64/8=8.0\text{ m})
Total = (6.4+8.0=14.4\text{ m}). - Wet asphalt:
(8.0^2/(2\times2.5)=64/5=12.8\text{ m})
Total = (6.4+12.8=19.2\text{ m}). - Against the 15 m marker: dry stops 0.6 m before the marker, so there is only a small margin. Wet overshoots by (19.2-15=4.2\text{ m}), so a collision would occur.
2. The student says the wet-road test shows the tyres are the main problem. Evaluate this by comparing the effect of reducing speed to 6.0 m/s with the effect of the wet road.
Read the worked answer
- At 6.0 m/s: reaction distance = (6.0\times0.80=4.8\text{ m}).
- Dry braking at 6.0 m/s: (6.0^2/(2\times4.0)=36/8=4.5\text{ m}), total 9.3 m.
- Wet braking at 6.0 m/s: (6.0^2/(2\times2.5)=36/5=7.2\text{ m}), total 12.0 m.
- Compare changes from the original 8.0 m/s wet case (19.2 m):
- Wet road at 8.0 m/s increases total from 14.4 m to 19.2 m, a rise of 4.8 m (+33%).
- Reducing speed to 6.0 m/s on the wet road reduces total from 19.2 m to 12.0 m, a fall of 7.2 m (-37.5%).
- So speed reduction has the larger effect in this comparison. Braking distance depends on (v^2), so a small speed reduction cuts kinetic energy and braking distance substantially. The wet road lowers friction and deceleration, and smooth tyres are still unsafe, but speed is the bigger controllable factor here.
3. Recommend two changes and justify them using the calculations.
Read the worked answer
- Reduce speed in wet conditions, for example to 6.0 m/s. This gives a total stopping distance of 12.0 m, leaving a 3.0 m margin before the 15 m marker. At 8.0 m/s on wet asphalt the bike needs 19.2 m, so the reduction is decisive.
- Replace or improve the smooth tyres. Tread helps water escape and maintains friction, which could increase the wet deceleration towards the dry value. If wet deceleration rose to 4.0 m/s² at 8.0 m/s, braking distance would be 8.0 m and total 14.4 m, just inside 15 m. However, that still leaves only 0.6 m, so better tyres should be combined with lower speed.
- Also increase following distance and stay alert: reaction time of 0.80 s at 8.0 m/s already uses 6.4 m before the brakes act. The calculations show that both reaction distance and braking distance matter, so riding slower and anticipating hazards is safer than relying on brakes alone.