Student sliding bag along floor in elevator

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Homework Statement
Pls see below
Relevant Equations
Pls see below
For this problem,
Printed physics problem text: a student in an elevator accelerating upward with acceleration a kicks a backpack at t = 0 with speed v; the backpack slides across the floor and hits the opposite wall a distance L away; find the coefficient of kinetic friction between backpack and elevator floor.

The solution is,
Handwritten-style worked solution: forces on a sliding backpack in the Earth frame, n = m(g+a), fk = k m(g+a), and L = vt + (1/2)ax t^2 with the (1/2)ax t^2 term circled in red, then solving for mu_k = 2(vt - L)/((g+a)t^2).

However, is the reason why they don't do ##-0.5a_xt^2## because the negative of the acceleration has already taken care of itself?

Many thanks!
 
The answer seems to make
[tex]a_x=-\alpha_k (g+a)<0[/tex]
negative. You can make it positve one with your setting of ##-0.5a_xt^2##.
 
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anuttarasammyak said:
The answer seems to make
[tex]a_x=-\alpha_k (g+a)<0[/tex]
negative. You can make it positve one with your setting of ##-0.5a_xt^2##.
Than you for your reply @anuttarasammyak !
 
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