Aforce of 400 newtons stretches a spring 2 meters. a mass of 50 kilograms is attached

If we start taking into account the free body diagram, we then start damping motion of a body by means of this equation:
m * d^2 x/dt^2 + c* dx/dt + k* x = 0 

free undamped motion is when (c =0) 
therefore 
50* d^2 x/dt^2 + 200* x = 0 
w = omega = sqrt(k/m) = sqrt(200/50) = 2 

Then  

A*cos(w*t) + B*sin(w*t) = x 

find A and B using intial conditions and you will get the rest that you need. Hope this helps

Given a certain formula, you simply need to plug in the three variables available to find the fourth, time, that you need.

V(final) = V(initial) + a (acceleration) × t (time)

Vf = 16m/s
Vi = = 6.5m/s
a = 3.6 m/s^2

16 = 6.5 + 3.6 × t

9.5 = 3.6 × t

t (time) = 2.64 seconds