Problem Statement:
A rocket with a mass of 2×10^4 kg is launched with a force of 5×10^5 N applied for a duration of 20 seconds. We need to calculate the velocity obtained by the rocket at the end of the 20th second.

Solution:
To calculate the velocity obtained by the rocket at the end of the 20th second, we can use Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.

Step 1: Calculate the acceleration:
We can use the formula:
Acceleration (a) = Force (F) / Mass (m)
Given that the force is 5×10^5 N and the mass is 2×10^4 kg, we can substitute these values into the formula:
a = (5×10^5 N) / (2×10^4 kg)
a = 25 m/s^2

Step 2: Calculate the change in velocity:
We know that acceleration is the rate of change of velocity with time. Since the force is applied for 20 seconds, the change in velocity (∆v) can be calculated using the formula:
∆v = a × t
where t is the time (20 seconds) and a is the acceleration (25 m/s^2).
∆v = (25 m/s^2) × (20 s)
∆v = 500 m/s

Step 3: Calculate the final velocity:
The final velocity (v) can be calculated by adding the change in velocity (∆v) to the initial velocity (u) of the rocket, which is assumed to be zero.
v = u + ∆v
v = 0 + 500 m/s
v = 500 m/s

Answer:
The velocity obtained by the rocket at the end of the 20th second is 500 m/s.

Is the answer 500m/s?