When the body remains stationary on the floor of the car, let's consider the following free-body diagram of the body:

The formula to calculate the Newtonian force on the body is given by

$F=m{a}_{\max } ...\left(1\right)$

And, the frictional force on the body by the surface of the car is given by

$f={\mu }_{s}mg ...\left(2\right)$

Equate equations (1) and (2) and simplify to obtain the required maximum acceleration of the car.

$\begin{array}{rcl}m{a}_{\max }& =& {\mu }_{s}mg\\ & \Rightarrow & a_{\max }={\mu }_{s}g ...\left(3\right)\end{array}$

Substitute the values of the known parameters into equation (3) to calculate the required parameter.

$\begin{array}{rcl}{a}_{\max }& =& 0.15\times 10 \mathrm{m} {\mathrm{s}}^{-2}\\ & =& 1.5 \mathrm{m} {\mathrm{s}}^{-2}\end{array}$