Question

74/75 (25 Pts) 1. A car traveling at an initial speed vrounds a bend in the road and sees that a dog is standing at rest in the middle of the road at a distance D in front of the car. After a short reaction time At, the driver slams on the brakes (at x = 0,t=0), and the car decelerates at a constant rate ac. (8) a. Find the speed of the car v(t) First seas dog and the position of the car x(t) fort > 0. (8) b. Find the time ts and the position of the car x(ts) when the car stops. starts to decelerate (9) c. Show that the maximum speed VM at which the car could have been initially moving and not hit the dog is given by +so VM = -acAt + [CacAt)+ 2Dac)/2 as ves? Vi= vi - treacheron (Vi-tm = Di. ve - Vil za D need v(t) hot Vf Vf² =2aD, + Virt Ive = Na Di tui + corrent units position D-(0o. At reachen) positum= D. a= b) vir V6²-Up = 2ax Ve- visat, o-vozacot t? / (or - Vo² = 2(0) .x = x t when cor = position of ear when stopped stops (c) 14 -not Ve-Vi = zax (0) - Vi² =2(a.) (0) - vi Villa (.) Vi = N-2 (0.) (Di) Vi= N2(a.)(D-(In. Atrachen s

Answer 1