Question

Nardine is traveling southbound on a level section of the I5 freeway with speed v₀ = 60mi/h. Joshua is also traveling southbound a distance d directly behind Nardine with the same speed v₀ = 60mi/h. Nardine has ABS brakes in her car, while Joshua does not have ABS brakes in his car. On this section of the freeway, Nardine's tires have coefficients of friction of
(us, jik) = (0.7,0.5)
and Joshua's tires have coefficients . Nardine suddenly notices something blocking the road in front of her and slams on her brakes. Suppose that Joshua's reaction time is t_R = 0.250s. What is the minimum safe distance d_min that the front of Joshua's car needs to be from the back of Nardine's car in order to avoid Joshua crashing into Nardine?

Answer 1

- car. LIH UK=0,3 Sance Nardine has ABS in her it loru not skid .: 09-41892-0.7x9.8 mle. Joshua YVO-60 muth 74 Nardine U2017 Vo = 60 min. = 26.8 m/s Vf zoml Li Distance travelled by Nardine Vo = 60 min before stopping y = V0 + 2004 1 0=(26.832 2X0.7%9.8.200 si XN = 52.kms 3) Distance Wavelled by Jodhtia before shopping og axit x2 3x4 = Vot 24-26.82x0.250) m 04-6.7 m Distance covered before applying brakes. and Quen accelerahon q Joshua, Ag -0389.8 mi? i 14?=10+2Q; Ya => 0 =(26.82/?_ 280-389-5 X2 3 X2= 122.35m .! X5 = (6.7+122.35)m = 12.9 m . i Minimum saje diatanie down = (y --Y) down =(129-52.4) m = 76.6m it down = 766 meter or diwn=0.0476 miles