To calculate the force required to accelerate an object, you can use Newton's second law of motion, which states:
\[ F = m \cdot a \]
Where:
- \( F \) is the force in newtons (N),
- \( m \) is the mass of the object in kilograms (kg),
- \( a \) is the acceleration in meters per second squared (m/s²).
Given:
- Mass \( m = 12 , \text{kg} \)
- Acceleration \( a = 65 , \text{m/s}^2 \)
Now, substitute the values into the formula:
\[ F = 12 , \text{kg} \times 65 , \text{m/s}^2 \]
\[ F = 780 , \text{N} \]
Therefore, the force required to accelerate a 12 kg object by \( 65 , \text{m/s}^2 \) is \( 780 , \text{N} \).