Let the initial speed be v0, then under braking we have:

v' = -16 ft/s^2

so:

v = -16 t + v0

and so the vehicle comes to rest at t=v0/16 s.

Now let x be the distance travelled since braking started then:

x' = v = -16 t + v0

so:

x = -8 t^2 + v0 t + x0,

but x0=0 here so:

x = -8 t^2 + v0 t

As the vehicle stops after 200ft we know that:

200 = -8 (v0/16)^2 + v0 (v0/16)

simplifying gives v0^2 = 6400, and so v=80 ft/s

RonL