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Let us assume the train was at rest at the start of the problem then

 v_{initial} = 0

The given data is the final velocity which 20m/s and the distance covered which is 150m. we can solve for the time it took the train to cover 150m by :

s =  \frac{d}{t} \\ 20 =  \frac{150}{t} \\ t =  \frac{150}{20} \\ t = 7.5s

then to get the acceleration;

use the formula :
v_{f} = v_{o} + at \\ 20 = 0 + a(7.5) \\ a =  \frac{20}{7.5} \\ a = 2.67  \frac{m}{s^{2} }

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