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

$a=3+2=5m/s^2$Solution in inertial frame :
 
The acceleration of the man in inertial frame is
or  $\overrightarrow{a}={\left[{\overrightarrow{a}}_{man}\right]}_{car}+{\left[{\overrightarrow{a}}_{car}\right]}_{inertialframe}$
 
From Newton’s second law 
or  $\overrightarrow{F}=m\overrightarrow{a}F=70\times 5=350N$
Solution in non-inertial frame
 
The acceleration of the man with respect to car is 2 m/s2 Now from Newton’s second law,  we can write,
 $\begin{array}{l}F-70\times 5=70\times 3\\ \therefore F=350N\end{array}$