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

$\\ \sf\longmapsto v=\dfrac{dx}{dt}$

$\\ \sf\longmapsto vdt=dx$

• 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 .

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

$\\ \sf\longmapsto ut+\dfrac{1}{2}at^2=(x-x_0)$

$\\ \sf\longmapsto x=x_0+ut+\dfrac{1}{2}at^2$