We are given that an object has an acceleration of 6 m/s^2. According to Newton's second law we have that the force is the product of the mass by the acceleration:
[tex]F=ma[/tex]Where:
[tex]\begin{gathered} F=\text{ force} \\ m=\text{ mass} \end{gathered}[/tex]We can solve for the acceleration by dividing both sides by the mass:
[tex]\frac{F}{m}=a[/tex]Since the original acceleration is 6 m/s^2 we have:
[tex]\frac{F}{m}=6\frac{m}{s^2}[/tex]Now, for the new acceleration, we are given that the new force is 3 times the original force and the mass is double the original mass, therefore, we can substitute:
[tex]\frac{3F}{2m}=a[/tex]But, we already established that:
[tex]\frac{F}{m}=6[/tex]Therefore:
[tex]\frac{3}{2}(6\frac{m}{s^2})=a[/tex]Therefore, solving the operations, the new acceleration is:
[tex]9\frac{m}{s^2}=a[/tex]Therefore, the acceleration is 9 meters per second squared.
