Question

Derive the formula v= u+ at
please derive in detail ​

Answer 1

Lets do

We know

The rate of change of velocity is acceleration .

`\\ \sf\longmapsto a=(dv)/(dt)`

`\\ \sf\longmapsto dv=adt`

Integrate both sides

`\\ \sf\longmapsto \int dv=a\int dt`

As acceleration is constant .Take it outside of integral .On velocity we can take limit u to v and time from 0 to t

`\\ \sf\longmapsto {\displaystyle{\int}}^v_u dv=a{\displaystyle{\int}}^t_0 dt`

Hence

`\\ \sf\longmapsto v{\huge}^v_u=at`

`\\ \sf\longmapsto v-u=at`

`\\ \sf\longmapsto v=u+at`