The speed of the body in the second half of the path is twice that of the first.

The speed of the body in the second half of the path is twice that of the first. Find these speeds if the average speed is 12 m / s.

Given: V (average speed) = 12 m / s; V2 (speed on the second half of the trip) = 2V1 (speed on the first half of the trip).

1) Speed on the first half of the journey: V = S / (t1 + t2) = S / (0.5S / V2 + 0.5S / V1) = 1 / (1 / 2V2 + 1 / 2V1) = 1 / (1 / 4V1 + 1 / 2V1) = 1 / (3 / 4V1), whence we express: 3 / 4V1 = 1 / V and V1 = V * 3/4 = 12 * 3/4 = 9 m / s.

2) Speed on the second half of the path: V2 = 2V1 = 2 * 9 = 18 m / s.

Answer: The velocities of the body in the first and second half of the path are respectively equal to 9 m / s and 18 m / s.