Question

The driver of a car slams on the brakes when he sees a tree blocking the road. The car slows uniformly with acceleration of -5.35 m/s² for 4.00 s, making straight skid marks 61.5 m long, all the way to the tree. With what speed does the car then strike the tree?

Answer 1

v^2 - u^2 = - 2*5.50*64.3, and
[(v+u)/2]*4.15 = 64.3, or Dividing first by second equation we get
[2*(v-u)]/4.15 = -11.2 or
v - u = -23.52; second equation can be written as
v+u = 29.71 or
2v = 6.194 or v = 3.097 or 3.10 m/s
Car strikes the tree with 3.10 m/s

Answer 2

let Vo be the intial velocity

x = Vot +0.5 a t²

(x - 0.5 a t²)/t = Vo = 26.1 m/s

final velocity V =Vo +at = 26.1 - 5.35x4 = 4.7m/s

so the car would hit the log with a speed of 4.7m/s