Question

S=ut+1/2at Sq. Prove By calculus method

Answer 1

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Answer 2

Derivation of $s = ut + \frac{1}{2} at^{2}$ by calculus method:

• Velocity is rate of change of displacement.

                        v = $\frac{ds}{dt}$             --------------(1)

• From first equation of motion, we have

                        v = u + at

                        $\frac{ds}{dt}$ = u + at                          [from (1)]

                        ds = udt + atdt

        Integrating on both sides

                     $\int\ {ds} = u\int\ dt + a\int\ t dt$           [u, a are constants]

                         $s = ut + a\frac{t^{2} }{2} + c$

          At t = 0, s = 0 ⇒ c = 0

                      ∴ $s = ut + \frac{1}{2} at^{2}$