# The first third of the way the body moved with a speed of V1 = 20 m / s, the second third

**The first third of the way the body moved with a speed of V1 = 20 m / s, the second third – with a speed of V2 = 12 m / s and the last third – with a speed of V3 = 2 m / s. Determine the average speed of the body**

V1 = 20 m / s.

V2 = 12 m / s.

V3 = 2 m / s.

S1 = S2 = S3 = S / 3.

Vav -?

To find the average speed of movement of the body Vav, it is necessary to divide the entire path S passed by it by the time of its movement t: Vav = S / t.

The travel time of the entire path is expressed by the sum: t = t1 + t2, where t1 is the time of movement on the first third of the path, t2 is the time of movement on the second third of the path, t3 is the time of movement on the third part of the path.

t1 = S1 / V1 = S / 3 * V1.

t2 = S2 / V2 = S / 3 * V2.

t3 = S3 / V3 = S / 3 * V3.

t = S / 3 * V1 + S / 3 * V2 + S / 3 * V3 = (S * V2 * V3 + S * V1 * V3 + S * V1 * V2) / 3 * V1 * V2 * V3 = S * (V2 * V3 + V1 * V3 + V1 * V2) / 3 * V1 * V2 * V3.

Vav = S * 3 * V1 * V2 * V3 / S * (V2 * V3 + V1 * V3 + V1 * V2) = 3 * V1 * V2 * V3 / (V2 * V3 + V1 * V3 + V1 * V2).

Vav = 3 * 20 m / s * 12 m / s * 2 m / s / (12 m / s * 2 m / s + 20 m / s * 2 m / s + 20 m / s * 12 m / s) = 4.7 m / s.

Answer: the average speed of body movement is Vav = 4.7 m / s.