The body moved one third of the way at a speed of 5 m / s. Determine the speed of the body along

The body moved one third of the way at a speed of 5 m / s. Determine the speed of the body along the rest of the path, if the average speed along the entire path is 7.5 m / s.

Initial data: V1 (body speed at 1/3 of the way) = 5 m / s; Vav. (average body speed along the entire path) = 7.5 m / s; S1 = 1/3 S; S2 = 2/3 S.

We find the speed of the body on the rest of the path from the following formula:

Vav. = S / (t1 + t2) = S / (1/3 S / V1 + 2/3 S / V2) = 1 / (1 / 3V1 + 2 / 3V2).

7.5 = 1 / (1 / (3 * 5) + 2 / 3V2).

1 / 7.5 = 1/15 + 2 / 3V2.

2 / 3V2 = 1 / 7.5 – 1/15 = 1/15.

3V2 / 2 = 15.

3V2 = 30.

V2 = 30/3 = 10 m / s.

Answer: On the rest of the path, the body moved at a speed of 10 m / s.