To calculate the final momentum of the mass after a force has acted on it, we can use the following steps:
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Calculate the acceleration (a) using Newton's second law of motion: \[ F = m \cdot a \] where:
- \( F \) = force (5 N)
- \( m \) = mass (5 kg)
Rearranging gives: \[ a = \frac{F}{m} = \frac{5 , \text{N}}{5 , \text{kg}} = 1 , \text{m/s}^2 \]
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Calculate the change in velocity (∆v) using the formula: \[ \Delta v = a \cdot t \] where:
- \( t \) = time (5 seconds)
So: \[ \Delta v = 1 , \text{m/s}^2 \cdot 5 , \text{s} = 5 , \text{m/s} \]
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Determine the final velocity (v) of the mass. Since it starts from rest (initial velocity \( u = 0 \)): \[ v = u + \Delta v = 0 + 5 , \text{m/s} = 5 , \text{m/s} \]
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Calculate the final momentum (p) using the formula: \[ p = m \cdot v \] Substituting the mass and final velocity: \[ p = 5 , \text{kg} \cdot 5 , \text{m/s} = 25 , \text{kg m/s} \]
Thus, the final momentum of the mass is \( \boxed{25 , \text{kg m/s}} \).