Lets do
We know
The rate of change of velocity is acceleration .
[tex]\\ \sf\longmapsto a=\dfrac{dv}{dt}[/tex]
[tex]\\ \sf\longmapsto dv=adt[/tex]
Integrate both sides
[tex]\\ \sf\longmapsto \int dv=a\int dt[/tex]
As acceleration is constant .Take it outside of integral .On velocity we can take limit u to v and time from 0 to t
[tex]\\ \sf\longmapsto {\displaystyle{\int}}^v_u dv=a{\displaystyle{\int}}^t_0 dt[/tex]
Hence
[tex]\\ \sf\longmapsto v{\huge{|}}^v_u=at[/tex]
[tex]\\ \sf\longmapsto v-u=at[/tex]
[tex]\\ \sf\longmapsto v=u+at[/tex]
