The body path is split into equal segments. The body begins to move with uniform acceleration and goes through

The body path is split into equal segments. The body begins to move with uniform acceleration and goes through the first segment in 1 s. In how many seconds does the body go through the ninth segment?

Given:

S1 = S – the length of the first segment of the path;

t1 = 1 second – the time during which the body passes the first segment of the path;

S2 = 9 * S – the length of the ninth segment of the path.

It is required to find the time t2 (seconds) during which the body will pass the ninth segment of the path.

According to the condition of the problem, the body moves uniformly accelerated without initial velocity. Then:

S1 = a * t1 ^ 2/2 from here:

a = 2 * S1 / t1 ^ 2 = 2 * S / 1 ^ 2 = 2 * S.

S2 = a * t2 ^ 2/2 hence:

t2 = (2 * S2 / a) ^ 0.5 = (2 * 9 * S / 2 * S) ^ 0.5 = 9 ^ 0.5 = 3 seconds.

Answer: the body will cover the ninth leg of the path in 3 seconds.