The net vertical force on the object is
∑ F[vertical] = n - mg = 0
where n is the magnitude of the normal force exerted by the surface, m is the object's mass, and g is the mag. of acceleration due to gravity. It follows that
n = mg = (25 kg) (9.8 m/s²) = 245 N
The net horizontal force is
∑ F[horizontal] = 300 N - f = ma
where f is the mag. of friction and a is the object's acceleration.
We have
f = µn
where µ is the coefficient of friction. Since the object starts at rest, it won't move and accelerate unless the applied force of 300 N is sufficient to overcome the maximum static friction, which is
f = 0.50 n = 0.50 (245 N) = 122.5 N
Since f < 300 N, the box will begin to slide, at which point the coefficient of kinetic friction kicks in and the mag. of friction is
f = 0.30 n = 0.30 (245 N) = 73.5 N
Now solve for a :
300 N - 73.5 N = (25 kg) a
a = (226.5 N) / (25 kg)
a = 9.06 m/s² ≈ 9.1 m/s²
