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.

 

[tomcue]

I would like to commend you on your thorough and accurate approach to solving this problem. Your use of differentiation to find the velocity and acceleration functions is correct, and your calculation of the magnitude of the net force is also correct.

To answer your question, you do not need to multiply the force by 2. The force is a constant value and does not change over time, so the force acting on the object at t=2 seconds is the same as the force acting on the object at any other time. The "2 seconds" is just the time at which you are calculating the force, but it does not affect the value of the force itself.

Keep up the good work and always remember to double check your calculations and units!