When a car traveling at speed v₁ rounds a corner, the driver sees another car traveling at a slower speed v₂ a distance d ahead.

(a) If the maximum acceleration the driver’s brakes can provide is a, show that the distance d must be greater than (v₁ - v₂)²/(2a) if a collision is to be avoided.

(b) Evaluate this distance for v₁ = 90 km/h, v₂ = 45 km/h, and a = 6 m/s².

(c) Estimate or measure your reaction time and calculate the effect it would have on the distance found in part (b).