First thing's first, we need to find the Net Force of the system in order to solve for acceleration. Gravity and Normal Force cancel out, so we don't really have to worry about anything on the y-axis. However, looking at the x-axis, we see two forces: the Force of the push and Frictional Force.
This means that:
[tex]F_{net}[/tex] = 500 - 100
[tex]F_{net}[/tex] = 400 (N)
Recall that Force = Mass * Acceleration. Since we have the Force and Mass, we can easily solve for Accel:
F = ma
a = [tex]\frac{F}{m}[/tex]
Plug the net force and mass into the equation:
a = [tex]\frac{F}{m}[/tex]
a = [tex]\frac{400}{50}[/tex]
a = 8 (m/[tex]s^{2}[/tex])
The box's acceleration is 8 m/[tex]s^{2}[/tex]
If you have any questions about how I got to the answer, just ask :)
