Uniform Retardation

Let u be the initial velocity

a be the uniform acceleration.

First 30 seconds:

By s = ut + 1/2 at^2

500 = 30u + 1/2 a(30)^2

50 = 3u + 45a ... (1)

By v = u + at

v = u + 30a ... (2)

This is the speed of the train just after 30 seconds

For the next 40 seconds:

By s = vt + 1/2 at^2

500 = (u + 30a)(40) + 1/2 a(40)^2

25 = 2u + 60a + 40a

25 = 2u + 100a ... (3)

Solving (1) and (3):

u = 18.45 m/s, a = -0.119 m/s^2

By equation of motion:

v^2 = u^2 + 2as

0 = (18.45)^2 + 2(-0.119)s

Distance travelled, s = 1.43 X 10^3 m

So, the further distance = 1.43 X 10^3 - 1000 = 430 m