Question

Derivation of s= u+ 1/2 at2​

Answer 1

We know that

Velocity is given by the rate of change of position w.r.t time

`\\ \sf\longmapsto v=(dx)/(dt)`

`\\ \sf\longmapsto vdt=dx`

• Now we can see in above v is not independent of t .So we replace the value of v by v=u+at and we get

`\\ \sf\longmapsto (u+at)dt=dx`

• Integrate with limits 0 to t and x_o to x respectively .

`\\ \sf\longmapsto u{\displaystyle{\int}_0^t}dt+a{\displaystyle{\int}_0^t}dt={\displaystyle{\int}^x_(x_0)}dx`

`\\ \sf\longmapsto ut+(1)/(2)at^2=(x-x_0)`

`\\ \sf\longmapsto x=x_0+ut+(1)/(2)at^2`