The machine as shown has 2 rods of length 1 m connected by a pivot at the top. The end of one rod is connected to the floor by a stationary pivot and the end of the other rod has a roller that rolls along the floor in a slot. As the roller goes back and forth, a 2 kg weight moves up and down. If the roller is moving towards right at a constant speed, the weight moves up with a:

Relation between horizontal position and vertical height is obtained by the Pythagorean theorem, and differentiating gives the velocity relation.

Given: $$L = 1\text{ m}$$,

$$\frac{dx}{dt} = -v_x\text{ (constant speed)}$$

$$\left(\frac{x}{2}\right)^2 + y^2 = 1 \implies \frac{x^2}{4} + y^2 = 1$$

Differentiating with respect to time:

$$\frac{2x}{4}\frac{dx}{dt} + 2y\frac{dy}{dt} = 0$$

$$\frac{x}{2}(-v_x) + 2y(v_y) = 0$$

$$v_y = \frac{x}{4y}v_x$$

As the roller moves right:

$$x \text{ decreases and } y \text{ increases} \implies \frac{x}{4y} \text{ decreases}$$

$$v_y \text{ decreases continuously}$$