Answer
The maximum acceleration that the plane can have is $2.94m/s^2$.
Work Step by Step
The maximum force that the plane can act upon the cup without making it slide backward cannot surpass the maximum static frictional force: $$F_{max}=f_s^{max}=\mu_sF_N=\mu_smg$$
$\mu_s$: coefficient of static friction
$m$: mass of the cup
$g$: gravitational acceleration
According to Newton's 2nd Law, we also have $$F_{max}=ma_{max}$$
$a_{max}$: maximum acceleration of the plane so that the cup does not slide
Therefore, $$ma_{max}=\mu_smg$$ $$a_{max}=\mu_sg=0.3\times9.8=2.94m/s^2$$
