Take the direction of motion to be the positive direction. The crate slows to a rest from 30.0 m/s in a matter of 5.0 s, so it has acceleration a such that
0 = 30.0 m/s + a (5.0 s) → a = -6.0 m/s²
At the moment its speed is 0, the crate has a net force of s + f acting in negative direction, where s and f denote the magnitudes of the stopping force (s = 250 N) and the friction force, respectively. By Newton's second law, we have
(-s) + (-f) = (100 kg) (-6.0 m/s²)
250 N + f = 600 N
f = 350 N
The friction force is proportional to the normal force by a factor of µ, the coefficient of kinetic friction. There is no movement in the up- and downward directions, so Newton's second law says
(-w) + n = 0
where w is the weight of the crate and n is the magnitude of the normal force. So
n = w = (100 kg) (9.80 m/s²) = 980 N
Then
f = µ n
350 N = µ (980 N)
µ = (350 N) / (980 N) ≈ 0.357
