We're asked to find the magnitude and direction of the acceleration of an object, given its mass and two forces that act on it.

To do this, we'll split the problem into #x#- and #y#-components, so we have

#F_(1x) = 5# #"N"#

#F_(1y) = 3# #"N"#

#F_(2x) = 2# #"N"#

#F_(2y) = 9# #"N"#

We can add respective components to find the **net force** components:

#sumF_x = F_(1x) + F_(2x) = 5# #"N"# #+ 2# #"N"# #= color(red)(7color(white)(l)"N"#

#sumF_y = F_(1y) + F_(2y) = 3# #"N"# #+ 9# #"N"# #= color(green)(12color(white)(l)"N"#

Now, we use Newton's second law to find the components of the object's *acceleration*:

#a_x = (sumF_x)/m = color(red)(7color(white)(l)"N")/(14color(white)(l)"kg") = color(purple)(0.5color(white)(l)"m/s"^2#

#a_y = (sumF_y)/m = color(green)(12color(white)(l)"N")/(14color(white)(l)"kg") = color(orange)(6/7color(white)(l)"m/s"^2#

The magnitude of the acceleration is thus

#a = sqrt((a_x)^2 + (a_y)^2) = sqrt((color(purple)(0.5color(white)(l)"m/s"^2))^2 + (color(orange)(6/7color(white)(l)"m/s"^2))^2#

#= color(blue)(0.993# #color(blue)("m/s"^2#

and the direction is

#theta = arctan((a_y)/(a_x)) = arctan((color(orange)(6/7color(white)(l)"m/s"^2))/(color(purple)(0.5color(white)(l)"m/s"^2))) = color(blue)(59.7^"o"#