A question

Maybe some thing is missing in your question =)

car A is moving at a uniform speed of 20m/s
car B is initially at rest
(a)
In order for car B to overtake car A before car A JUST passes the finishing line
car B accelerates at an acceleration of 5ms^-2
the time taken for car A to reach the finishing line = t
the time taken for car B to reach the finishing line = t

Let the distance from car A to the finishing line be d metres
so the distance from car A to the finishing line also be d metres
d = ua * t where ua = speed of car A = 20 m/s
d = 20t

d = ub * t + 1/2 * a * t^2 where ua = initial speed of car B = 0 m/s
d = 1/2 * 5 * t^2

20t = 5/2 * t^2
t = 8 or 0 (rejected) as t = 0 is the initial position
so the time taken for car B to reach the finishing line is 8 seconds

(b)
the time taken for car A to reach the finishing line is also 8 seconds

(c)
Both cars will pass the finishing line at the same time as inital assumption

(d)
In order for both cars to reach the finishing line at the same time, the acceleration of car B is 5ms^-2

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N.B.
If any more conditions given in the question, like the distance from car A to the finishing line etc, the answer to this question is different.

I hope this can help your understanding. :)