A body started from rest and moving with uniform acceleration a then the change in velocity after producing one unit displacement is equal to

We know for a body started from rest and moving with uniform acceleration a

The change in velocity after travelling through s is $\text{v}=\sqrt{2as}$

Now we get change in velocity per unit displacement

i.e.$\frac{\text{v}}{\text{s}}=\frac{\sqrt{2as}}{s}=\sqrt{\frac{2a}{s}}$

We get change in velocity after producing unit displacement i.e. s = 1

We get$\text{v}=\sqrt{2a}$