Describe the mathematical relationship between acceleration and the mass

The mathematical relationship between acceleration (\(a\)), mass (\(m\)), and force (\(F\)) is described by Newton's second law of motion. This law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. The relationship can be expressed with the following equation: \[ F = m \cdot a \] Where: - \(F\) is the net force applied to the object (in newtons, N), - \(m\) is the mass of the object (in kilograms, kg), - \(a\) is the acceleration of the object (in meters per second squared, m/s²). From this equation, we can derive the following relationships: 1. **Acceleration and Force**: If the mass is constant, an increase in force will result in an increase in acceleration. This can be expressed as: \[ a = \frac{F}{m} \] 2. **Acceleration and Mass**: If the force is constant, an increase in mass will result in a decrease in acceleration. This can be expressed as: \[ a = \frac{F}{m} \] Here, if \(m\) increases, \(a\) decreases, assuming \(F\) remains constant. In summary, the relationship shows that acceleration is dependent on both the net force applied to an object and its mass.