To find the average speed of a body that travels from point A to point B with a velocity of 10 m/s and then returns from point B to point A with a velocity of 20 m/s, we can use the formula for average speed.
Average speed is defined as the total distance traveled divided by the total time taken.
Let's assume the distance from A to B is D.
The time taken to travel from A to B is given by: Time_1 = Distance / Velocity_1 = D / 10 m/s = D/10 seconds
The time taken to travel from B to A is given by: Time_2 = Distance / Velocity_2 = D / 20 m/s = D/20 seconds
The total distance traveled is 2D (going from A to B and then returning from B to A).
The total time taken is the sum of Time_1 and Time_2: Total Time = Time_1 + Time_2 = D/10 + D/20 = (2D + D) / 20 = 3D / 20 seconds
Now we can calculate the average speed: Average Speed = Total Distance / Total Time = 2D / (3D / 20) = (2D * 20) / (3D) = 40D / 3D = 40/3 m/s
Therefore, the average speed of the body is 40/3 m/s.