The question tells us that distance is directly proportional to the square of time
d ∝ t^2 as stated in the question (∝ means proportional to)
d = kt^2 (we use k as a constant in this. We use the constant since we don't know what the actual equation is.)
Our givens:
d = 16 when t = 1
Plugging this in to our equation, we get
16 = k (1)^2
k = 16
That means that d = 16t^2 is our equation
Pluggin our values in
When t = 5, d = 400 ft
when d = 256, t = 4
