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Sagot :
We know that
Velocity is given by the rate of change of position w.r.t time
[tex]\\ \sf\longmapsto v=\dfrac{dx}{dt}[/tex]
[tex]\\ \sf\longmapsto vdt=dx[/tex]
- 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
[tex]\\ \sf\longmapsto (u+at)dt=dx[/tex]
- Integrate with limits 0 to t and x_o to x respectively .
[tex]\\ \sf\longmapsto u{\displaystyle{\int}_0^t}dt+a{\displaystyle{\int}_0^t}dt={\displaystyle{\int}^x_{x_0}}dx[/tex]
[tex]\\ \sf\longmapsto ut+\dfrac{1}{2}at^2=(x-x_0)[/tex]
[tex]\\ \sf\longmapsto x=x_0+ut+\dfrac{1}{2}at^2[/tex]
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