To find the acceleration of the system consisting of the two gliders \( m_1 \) and \( m_2 \) connected by a string, we can use Newton's second law.
First, we need to calculate the total mass of the system:
\[ m_{\text{total}} = m_1 + m_2 = 2.0, \text{kg} + 0.5, \text{kg} = 2.5, \text{kg} \]
Next, we can use Newton's second law, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration (\( F = ma \)). In this case, the net force \( F \) is the force applied to \( m_2 \), and we can set it up as follows:
\[ F = m_{\text{total}} \cdot a \]
Substituting the values we have:
\[ 5.0, \text{N} = 2.5, \text{kg} \cdot a \]
Now, solve for \( a \):
\[ a = \frac{5.0, \text{N}}{2.5, \text{kg}} = 2.0, \text{m/s}^2 \]
Thus, the acceleration of the glider system is:
\[ \boxed{2.0, \text{m/s}^2} \]
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