Answer:
[tex]a=6.5m/s^2[/tex] to the left.
Explanation:
We can use the equation [tex]v=v_0+a(t-t_0)[/tex] where v is the velocity at time t and [tex]v_0[/tex] the velocity at [tex]t_0[/tex]. Since we want the acceleration we write this equation as:
[tex]a=\frac{v-v_0}{t-t_0}[/tex]
Considering the direction to the right as the positive one, we have [tex]v_0=+5m/s[/tex] at [tex]t_0=10s[/tex], and [tex]v=-8m/s[/tex] at [tex]t_0=8s[/tex], so we substitute:
[tex]a=\frac{v-v_0}{t-t_0}=\frac{(-8m/s)-(5m/s)}{(10s)-(8s)}=\frac{-13m/s}{2s}=-6.5m/s^2[/tex]
Where the minus sign indicates it is directed to the left.
