Speed after body slows down with negative acceleration.

[borovecm]

Homework Statement

Hi. I know this is a simple problem but i want to know if I am correct. Here it goes.
Body moves with speed 12 m/s. It starts to slow down with negative acceleration 2 m/s$$^{}2$$ for 8 meters. What is his speed after those 8 meters.

Homework Equations

s=(1/2)*a*t*t
v*v=2as
v=v' + at
s=v'*t + (1/2)*a*t*t

The Attempt at a Solution

s=(1/2)*a*t*t
t*t=2s/a=16/2=8
t=2,82

v=v' - at = 12-5,65=6,34 m/s
that's one solution the other would be.
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s=v'*t - (1/2)a*t*t
8=12*t - (1/2)*2*t*t
t*t - 12t +8 = 0
we get quadratic equation... we solve it and get two solutions.
t1=0,71 s
t2=11,29 s

we insert this into
v=v' - at
v1=10,58 m/s
v2=-10,58 m/s

this solution is probably the correct one. But why do we get 2 values for time?

 

[rl.bhat]

s=(1/2)*a*t*t
t*t=2s/a=16/2=8
t=2,82This formula is wrong. It should be s = ut + 1/2*at^2.
In the problem t is not given .So you have to use v^2 = u^2 -2as. for retarding motion.

 

[borovecm]

s=(1/2)*a*t*t
t*t=2s/a=16/2=8
t=2,82This formula is wrong. It should be s = ut + 1/2*at^2.
In the problem t is not given .So you have to use v^2 = u^2 -2as. for retarding motion.

Thanx. I understand.