Answer
We can rank the cars in order of the time that it takes them to stop, from smallest to greatest:
$d \lt b = c \lt a \lt e$
Work Step by Step
Since the force to bring the cars to rest has the same magnitude, the cars with less momentum will stop in less time than the cars with more momentum.
We can find the momentum of each car:
(a) $p = mv = (1500~kg)(30~m/s) = 45,000~kg~m/s$
(b) $p = mv = (1500~kg)(20~m/s) = 30,000~kg~m/s$
(c) $p = mv = (1000~kg)(30~m/s) = 30,000~kg~m/s$
(d) $p = mv = (1000~kg)(20~m/s) = 20,000~kg~m/s$
(e) $p = mv = (2000~kg)(40~m/s) = 80,000~kg~m/s$
We can rank the cars in order of the time that it takes them to stop, from smallest to greatest:
$d \lt b = c \lt a \lt e$
