Total stopping distance = Reaction distance + Braking distance
During reaction time (t_r): driver doesn't brake, car moves at speed v.
- Reaction distance: d_r = v * t_r
During braking (deceleration a):
- v^2 = 2ad_b => d_b = v^2/(2a)
Total: d = v*t_r + v^2/(2a)
Key insight: Braking distance is proportional to v^2. Doubling speed quadruples braking distance.
JEE application: If a car at 20 m/s stops in 50 m, find the deceleration. 0 = (20)^2 + 2a50 => a = -400/100 = -4 m/s^2