Calculate the maximum acceleration of a moving car so that a body...

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{cases}m{a}_\max & = & {\mu}_{s}mg \\ & ⇒ & {a}_\max = {\mu}_{s}g . . . \left(3\right)\end{cases}

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

\begin{cases}{a}_\max & = & 0 . 15 \times 10m{s}^{- 2} \\ = & 1 . 5m{s}^{- 2}\end{cases}