First convert from mi/h to ft/s. There are 5280 ft to 1 mi, and 3600 s to 1 h, so
36 mi/h = (36 mi/h) * (5280 ft/mi) * (1/3600 h/s) = 52.8 ft/s
Let a be the acceleration of the car. The car's speed at time t is
v = 52.8 ft/s + a t
so that after 5.4 s, it attains a speed of
v = 52.8 ft/s + (5.4 s) a
Recall that
v² - u² = 2 a ∆x
where u is the car's initial velocity and ∆x is the distance it's traveled.
We have
(52.8 ft/s + (5.4 s) a)² - (52.8 ft/s)² = 2 a (595 ft)
Omitting units, this equation reduces to
(52.8 + 5.4 a)² - 52.8² = 1190 a
==> 29.16 a² - 619.76 a = 0
==> 29.16 a - 619.76 = 0
==> 29.16 a = 619.76
==> a ≈ 21.25 ft/s²