Force F = 500 Newtons / unit length
mass / unit length of the system = 0.25 kg / meter = mass/length
acceleration a = F / m = 500 / 0.25
= 2,000 m/sec²
assuming that the force is acting uniformly along the length of the system.
velocity = u + a t = at if initial velocity u = 0, as the system starts from rest.
v = 2,000 t, where t = time.