Andy is waiting at the signal. as soon as the light turns green, he accelerates his car at a uniform rate of 8.00 meters/second2. what is the displacement of andy’s car after 30.0 seconds?

-- Accelerating at the rate of 8 m/s², Andy's speed
   after 30 seconds is

                                   (8 m/s²) x (30.0 s)  =  240 m/s .

-- His average speed during that time is

                                 (1/2) (0 + 240 m/s)  =  120 m/s .

-- In 30 sec at an average speed of 120 m/s,
   Andy will travel a distance of
                                                 (120 m/s) x (30 sec) = 3,600 m

                                                                                = 3.6 km .

"But how ? ! ?", you ask.

How in the world can Andy leave a stop light and then
cover 3.6 km = 2.24 miles in the next 30 seconds ?

The answer is:  His acceleration of  8 m/s², or about  0.82 G
is what does it for him.

At that rate of acceleration ...

-- Andy achieves "Zero to 60 mph" in 3.35 seconds,
   and then he keeps accelerating.

-- He hits 100 mph in 5.59 seconds after jumping the light ...
   and then he keeps accelerating.

-- He hits 200 mph in 11.2 seconds after jumping the light ...
   and then he keeps accelerating.

-- After accelerating at 8 m/s² for 30 seconds, Andy and his
   car are moving at  537 miles per hour !
   We really don't know whether he keeps accelerating,
    but we kind of doubt it. 

A couple of observations in conclusion:

-- We can't actually calculate his displacement with the information given.
   Displacement is the distance and direction between the starting- and
   ending-points, and we're not told whether Andy maintains a straight line
   during this tense period, or is all over the road, adding great distance
   but not a lot of displacement.

-- It's also likely that sometime during this performance, he is pulled
   over to the side by an alert cop in a traffic-control helicopter, and
   never actually succeeds in accomplishing the given description.