A man of mass $70 kg$ is running on a railroad car, which is going towards right with an acceleration of $m/s^2$ . The acceleration of man with respect to car is $3 m/s^2$ . Find the force acting on the man (in inertial frame).

In inertial frame:

The acceleration of the man in inertial frame is

                                     $\overrightarrow{a}={\left[{\overrightarrow{a}}_{man}\right]}_{car} + {\left[{\overrightarrow{a}}_{car}\right]}_{intertial frame}$

or                                   $$\begin{gathered} a=3+2 \\ =5 m/s^2 . \end{gathered}$$

From Newton's second law,

                                     $\overrightarrow{F} = m\overrightarrow{a}$

or                                  $F = 70\times 5=350 N$ .