**Calculating the Net Force**

To determine the velocity of the crate in 3 seconds, we need to first calculate the net force acting on the crate. The net force can be determined by subtracting the force of friction from the applied towing force.

The force of friction can be calculated using the formula:

Frictional Force = coefficient of kinetic friction * Normal Force

The normal force is equal to the weight of the crate, which can be calculated using the formula:

Weight = mass * acceleration due to gravity

In this case, the mass of the crate is 50 kg and the acceleration due to gravity is approximately 9.8 m/s^2. Therefore:

Weight = 50 kg * 9.8 m/s^2 = 490 N

The frictional force can be calculated as:

Frictional Force = 0.3 * 490 N = 147 N

The net force can now be determined:

Net Force = Applied Force - Frictional Force = 400 N - 147 N = 253 N

**Applying Newton's Second Law**

Now that we have the net force, we can apply Newton's second law of motion to calculate the acceleration of the crate. Newton's second law states that:

Net Force = mass * acceleration

Therefore, the acceleration can be calculated as:

Acceleration = Net Force / mass = 253 N / 50 kg = 5.06 m/s^2

**Calculating the Final Velocity**

Next, we can use the equation of motion to calculate the final velocity of the crate after 3 seconds. The equation of motion is:

Final Velocity = Initial Velocity + (Acceleration * Time)

Since the crate is initially at rest (i.e., the initial velocity is 0), the equation simplifies to:

Final Velocity = Acceleration * Time = 5.06 m/s^2 * 3 s = 15.18 m/s

Therefore, the velocity of the crate after 3 seconds is 15.18 m/s.

**In Summary**

To summarize, the velocity of the crate after 3 seconds can be calculated by determining the net force acting on the crate, applying Newton's second law to calculate the acceleration, and then using the equation of motion to calculate the final velocity. In this case, the net force is 253 N, the acceleration is 5.06 m/s^2, and the final velocity is 15.18 m/s.