Question

The "reaction time" of the average automobile driver is about 0.7 s . An automobile can slow down with an acceleration of 11.4 ft/s2 . (a) Compute the total distance covered in coming to a stop after a signal is observed from an initial velocity of 14.4 mi/h . (b) Compute the total distance covered in coming to a stop after a signal is observed from an initial velocity of 55.2 mi/h .

Answer 1

a)

initial velocity = 14 .4 mi/h = 21.12 ft/s

reaction time = t = 0.7 sec

so distance covered before actually applying the brakes in reaction time = d₁ = 21.12 x 0.7 = 14.8 ft

a = acceleration = - 11.4 ft/s²         since brakes are applied

Vf = final velocity = 0

d₂ = distance covered after applying brakes

Using the kinematics equation

V_f² = V_i² + 2 a d₂

0² = 21.12² + 2 (-11.4) d₂

d₂ = 19.6 ft

Total distance = 19.6 + 14.8 = 34.4 ft

b)

initial velocity =V_i = 55.2 mi/h = 80.96 ft/s

reaction time = t = 0.7 sec

so distance covered before actually applying the brakes in reaction time = d₁ = 80.96 x 0.7 = 56.7 ft

a = acceleration = - 11.4 ft/s²         since brakes are applied

V_f = final velocity = 0

d₂ = distance covered after applying brakes

Using the kinematics equation

V_f² = V_i² + 2 a d₂

0² = 80.96² + 2 (-11.4) d₂

d₂ = 287.5 ft

Total distance = 287.5 + 56.7 = 344.2 ft