To solve this problem we will apply the concepts related to Newton's second law for which the product of mass and acceleration is defined as the force applied to an object. Mathematically this is,
[tex]F_{net} = ma \rightarrow a = \frac{F_{net}}{m}[/tex]
Here,
[tex]F_{net} =[/tex] Net external Force
m = Mass of the body
a = Acceleration
The net force on the body would be given by the difference between the ascending force and the weight, therefore,
[tex]F_{net} = F-W[/tex]
Here,
F = Upward Force
W = Weight
The Weight is,
[tex]W = (2.78kg)(9.81m/s^2)[/tex]
[tex]W = 27.27N[/tex]
Then the [tex]F_{net}[/tex] is
[tex]F_{net} = 31.3-27.27[/tex]
[tex]F_{net} = 4.03N[/tex]
Finally replacing at the first equation we have,
[tex]a = \frac{4.03N}{2.78kg}[/tex]
[tex]a = 1.44m/s^2[/tex]
Therefore the acceleration of the stone is [tex]1.44m/s^2[/tex]
