Force acting on object of given coordinates

[Simply Is]

Homework Statement

3.0 kg object is moving in plane with x and y coordinates given by x=5t^2-1 and y=3t^2-2 where x and y are meters and t is seconds. Find magnitued of net force acting on object at t=2 seconds.

Homework Equations

(vectors above the letters where they normally go)
F=ma
a = ax + ay

The Attempt at a Solution

Taking the 2 equations, and differentiating to get the velocities functions, then again to get the acceleration functions I get (the i and j are "hats"):

Vx = 10t i and ax = 10 i
Vy = 6t i and ay = 6 j

a = ax + ay and magnitude a = sqrt (ax^2 + ay^2) = sqrt (10^2 + 6^2) = sqrt (136) = 11.66 m/s^2

Then inserting into F=ma:

F = (3.0 kg)(11.66 m/s^2)
F = 34.98 N

And I can just ignore the "2 seconds" because the same constant force is acting? Or do I need to multiply that force by 2?

Thank you for any guidance.

 

[rock.freak667]

what you have looks to be correct.