Plz solve this question

Solution
time taken by the train to reach the railway crossing will be

t =distance it has to travel / speed of the train  

so,

t = 1km /  90km/hr = 0.011 hours

or

t = 39.6 secs.

now, the car should reach the crossing in exactly this amount of time.

we know that

s = ut + (1/2)at² = 500m

or the acceleration required will be

a = 2(s - ut) / t² 

or

a = 2 (500 - 2x39.6) / 39.6²

or

a = 841.6 / 1568.16

so, the car must accelerate by

a = 0.536 m/s²

Final velocity
v² = u² + 2as
$$\begin{gathered} v^2 =2^2 + 2\times 0.536\times 500 \\ {v}^2 = 4+536 = 540 \\ v =23.23 m/s \end{gathered}$$