The displacement and the increase in the velocity of a moving...

Considering acceleration is constant, we can write

$v = u + at$

As increase in velocity in $1s$ is given as $50m{s}^{- 1}$, therefore

$⇒ a = 50m{s}^{- 2}$

Now, displacement covered between given time interval is, 

$125 = ut + \dfrac{1}{2}a{t}^{2}$

$⇒ 125 = u + \dfrac{a}{2}$

$⇒ u = 100m{s}^{- 1}$

Velocity after $1s$ will be, $v = 100 + 50 = 150m{s}^{- 1}$

Therefore, displacement covered in \left(t + 1\right)s\text{to}$\left(t + 2\right)s$ will 

$∴ S{n}^{th} = v{t}^{'} + \dfrac{1}{2}a{\left({t}^{'}\right)}^{2}, \text{where}{t}^{'} = 1s$

$= 175m$