Two weights of 7 and 11 kg hang at the ends of the thread, which is thrown over a fixed weightless block.

Two weights of 7 and 11 kg hang at the ends of the thread, which is thrown over a fixed weightless block. How long after the start of the movement of the loads, each of the weights will cover the path of 10 cm?

Given:
m1 = 7kg,
m2 = 11kg,
l = 10cm = 0.1m
g = 10m / s ^ 2;
Find: t -?
Let us find the acceleration a, with which the system of weights moves:
According to Newton’s second law:
m1 * a = T – m1 * g,
m2 * a = m2 * g – T;
here T is the thread tension;
If we add two equations, we get:
(m1 + m2) * a = (m2 – m1) * g;
a = g * (m2 – m1) / (m2 + m1) = 10 * 4/18 = 2.22m / s ^ 2;
Let us write the equation for uniformly accelerated motion without initial velocity
l = a * (t ^ 2) / 2;
From here
t = sqrt (2 * l / a) = sqrt (2 * 0.1 / 2.22) = 0.3s.