Question

derive 2nd equation of motion​

Answer 1

$\huge\sf\red{Answer}$

☞︎︎︎ Second equation of motion is :-

$\sf S = ut + \dfrac {1}{2} at^{2}$

☞︎︎︎ DERIVE :

we know that,

$\sf Displacement = \dfrac {Initial \: velocity \: + \: Final \: velocity}{2} \times Time.$

$\sf S \: = \dfrac \bigg({u + v}{2}} \bigg) \times t$

From first equation of motion,

we know that,

v = u + at

Now, putting the values in equation,

$\sf S \: = \dfrac \bigg({u + ( u + at)}{2}\bigg) \times t$

$\sf S \: = \dfrac \bigg({2u + at}{2} \bigg) \times t$

$\sf S \: = \bigg({ u + \dfrac {1}{2} at^{2} \bigg)$

$\sf S \: = \: ut + \dfrac {1}{2} at^{2}$

$\therefore$ Hence derived ✔️