Question

Derive the following equations of uniformly acclerated motion by calculus method.
(i) u + at = v,
(ii) s = ut + at2
(iii) v2 = u2 + 2ask​

Answer 1

Answer:

Derivation of the equation by the calculus method:-

we know that,

Acceleration, a=dtdv

or, ∫vu1dv=∫a01dt

or, V−u=at

or,v=u+at

−2

      

      a=dsVdV

      a=dsVdv

or,   ∫vuVdV=∫s0 ads

or,   v2(2)uv=as

or,   v2−u2=2as

3−

  putting v=u+at in equation 

            V2−u2,

  (u+at2)2−u2=2as

or, 2uat+a2t2=2as

or, s=ut+21at2