A quarter of the way the body’s speed is 4 m / s, and then until the end of the path the body

| February 18, 2021 | education

A quarter of the way the body’s speed is 4 m / s, and then until the end of the path the body moves at a speed of 2 m / s. what is the average body speed all the way?

V1 = 4 m / s.

V2 = 2 m / s.

S1 = S / 4.

Vav -?

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

t = t1 + t2.

t1 = S1 / V1 = S / 4 * V1.

Since the first part of the path is S1 = S / 4, the second part of the path is S2 = S – S1 = S – S / 4 = 3 * S / 4.

t2 = S2 / V2 = 3 * S / 4 * V2.

t = S / 4 * V1 + 3 * S / 4 * V2 = S * V2 + 3 * S * V1 / 4 * V1 * V2 = S * (V2 + 3 * V1) / 4 * V1 * V2.

Vav = S * 4 * V1 * V2 / S * (V2 + 3 * V1) = 4 * V1 * V2 / (V2 + 3 * V1).

Vav = 4 * 4 m / s * 2 m / s / (2 m / s + 3 * 4 m / s) = 2.3 m / s.

Answer: the average speed of body movement is Vav = 2.3 m / s.



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