Question

Equations of motion derivation calculus method.

Answer 1

v = ∫ a dt , v = at + C , v(0) = u , u = a * 0 + C , C = u , v = at + u , s = ∫ v dt , s = ∫ (at + u) dt , s = ½ at² + ut + c , s(0) = 0 , 0 = ½ a * 0² + u * 0 + c , c = 0 , s = ½ at² + ut , a = dv/dt , a = (dv/ds)(ds/dt) , a = v (dv/ds) , ∫ a ds = ∫ v dv , as = ½ v² + constant , v = u at s = 0 , a * 0 = ½ u² + constant , constant = -½ u² , as = ½ v² - ½ u² .

Answer 2

your answer is in the pic

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