Question

A truck is moving forward at a constant speed of 20m/s. The driver sees a car in front at 110m suddenly after a reaction time he applies a brake of acceleration of -3m/s.what Will be maximum reaction time to avoid collision? and what distance truck would move after brake applied?

Answer 1

Maximum allowable delta t to avoid collision and
distance will the truck have moved before the brakes take hold
V0 + a * ts = 0
ts 
= V0 / (-a)
ts = 20 / 3 = 6.67 s (the time needed to stop the truck)
Braking 
distance: S(ts) = V0* ts + a * ts^2 / 2 = 20 * 7 - 3 * 49 / 2
= 140 - 73.5 = 
66.5 m
deltaS = D - S(ts) = 110 - 66.5 = 43.5 m
deltaS = V0 * 
deltat
deltat = deltaS / V0
deltat = 43.5 / 20 = 2.175 s
Let deltat 
= 1.4 s.
l = D - S(ts) - V0* deltat
l = 110 - 66.5 - 20 * 1.4 = 15.5 m
t 
= deltat + ts
t = 1.4 + 7 = 8.4 s