Question

S is equal. . ut 1/2 at2 with calculus method...........no need silly answer​

Answer 1

AnswEr :

We have to derive s = ut + ½at² by calculus method

Consider the Velocity - Displacement Relation :

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

From the First Kinematic Equation,

$\sf \: v = u + at$

Thus,

$\sf \: u + at = \dfrac{dx}{dt} \\ \\ \longrightarrow \: \sf \: (u + at)dt = dx$

Integrating on both sides,

$\longrightarrow \displaystyle \: \sf \int _0^s{x}^{0} .ds \: = \int_0^tu {t}^{0}.dt + \int_0^tat.dt \\ \\ \longrightarrow \: \displaystyle \: \sf \: \int _0^s{x}^{0} .ds \: =u \int_0^t {t}^{0}.dt + a\int_0^tt.dt \\ \\ \longrightarrow \: \sf \: \bigg[x \bigg]_0^s = u\bigg[t \bigg]_0^t + a\bigg[ \dfrac{ {t}^{2} }{2} \bigg]_0^t \\ \\ \longrightarrow \: \sf \: (s - 0) = u(t - 0) + \dfrac{a}{2} ( {t}^{2} - {0}^{2} ) \\ \\ \large{ \longrightarrow \: \boxed{ \boxed{ \sf \: s = ut + \dfrac{1}{2} a {t}^{2} }}}$

Answer 2

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