Two loads of mass $m_1 = 2$ kg and $m_2 = 3$ kg are connected by a single string passing over a massless, inextensible pulley (an Atwood machine). Find the acceleration of the system. Neglect air resistance; $g = 10$ m/s².
Take the direction towards the larger load as positive ($m_2$ down, $m_1$ up). Write Newton's second law for each body:
$$m_2 g - T = m_2 a, \quad T - m_1 g = m_1 a$$
Add the equations to eliminate the tension $T$:
$$(m_2 - m_1) g = (m_1 + m_2) a$$
$$a = \frac{(m_2 - m_1) g}{m_1 + m_2} = \frac{(3 - 2) \cdot 10}{2 + 3} = \frac{10}{5} = 2 \text{ m/s}^2$$
$a = 2$ m/s²