College Physics.....please help me out.?

Question

The driver of a truck slams on the brakes when he sees a tree blocking the road. The truck slows down uniformly with acceleration -6.1 m/s2 for 4.20 s, making skid marks 64.3 m long that end at the tree. With what speed does the truck then strike the tree?

_____m/s

Thanks for any help!

Answer 1

d = V1t + (1/2)at^2

64.3 = V1(4.2) + (1/2)(-6.1)(4.2)^2

64.3 = 4.2V1 -53.802

118.102 = 4.2V1

28.1195238 = V1

(V2)^2 = (V1)^2 + 2ad

(V2)^2 = 28.12^2 + 2(-6.1)(64.3)

790.707596 - 784.46 = V2^2

6.24759 = V2^2

V2 = 2.5 m/s

Answer 2

first, figure out the initial speed from the data given using the equation:

dist = v0t +1/2 at^2, where dist is distance traveled (64.3m), v0 is the initial speed (to be determined) a is the accel (-6.1m/s/s) and t is the time of travel (4.2s)

solving:

64.3=4.2v0-1/2(6.1)(4.2)^2

64.3=4.2v0-53.8

v0=28.1 m/s

now, use the equation:

vf^2=v0^2+2ad to find the final speed:

vf^2=28.1^2+2(-6.1)(64.3)

vf^2=791-784=7

vf=sqrt[7]=2.65 m/s