how will the first equation of …

The equation of motion is derived based on the Newton’s laws of motion. And it changes accordingly when an object changes with uniform velocity.

Given is that object moves with uniform velocity, that is no change in velocity so there will no acceleration.

As we know {tex}a=v-\left(\frac{u}{t}\right) {/tex}

Here, u = v (due to uniform velocity)

{tex}\begin{aligned} a &=\frac{0}{t} \\ a &=0 \end{aligned}.{/tex}

1st equation of motion is, v = u + at

{tex}\begin{array}{l}{v=u+0 \times t} \\ {v=u}\end{array}{/tex}

2nd equation of motion, {tex}s=u t+\frac{1}{2} a t^{2}{/tex}

{tex}\begin{array}{l}{s=u t+\left(\frac{1}{2} \times 0\right) \times t^{2}} \\ {s=u t}\end{array}{/tex}

3rd equation of motion, {tex}\mathrm{v}^{2}=\mathrm{u}^{2}+2 \mathrm{a} \mathrm{s}{/tex}

{tex}\begin{array}{l}{\mathrm{v}^{2}=\mathrm{u}^{2}+2 \times 0 \times s} \\ {v^{2}=u^{2}}\end{array}.{/tex}