**Problem : **
A 10 kg mass, initially at rest, experiences three forces: one North
with magnitude 10 N, one East, with magnitude 20 N and one Northeast
with magnitude 30 N. Find the resulting acceleration. After 10 seconds,
assuming the forces continue to act while the object is in motion, what
is the object's velocity? How far has it traveled?

We solve the problem by drawing a free body diagram:

Solution 1

And sum these two vectors. The magnitude of the resultant force is given by:

And the direction is given by:

To find the final velocity and position of the object, we simply use the equations learned in kinematics:

Thus, after 10 seconds, the object is moving with a velocity of 51.7 m/s, directed 31.7 degrees North of East. Also, the object has moved 258.5 meters, in the same direction.