Rate of $S_{N}1$ tracks the stability of the carbocation formed when bromide leaves.

Structures (I) and (II) are bridgehead halides on rigid bicyclic frameworks. The resulting bridgehead carbocations cannot become planar (Bredt’s rule), so they are extremely high-energy and form only with great difficulty. Of the two, (I) has more $+I$ alkyl substitution around the bridgehead, so its cation is marginally less unstable than (II)’s: (II) $<$ (I).

(III) is tert-butyl bromide — gives a stable, planar tertiary carbocation, fast $S_{N}1$.

(IV) is trityl bromide — the triphenylmethyl cation is exceptionally stable due to resonance delocalisation across three phenyl rings. Fastest $S_{N}1$.

Overall: (II) $<$ (I) $<$ (III) $<$ (IV).