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Question

Deduce the equations of a uniformly accelerated motion in one dimension by calculus method.


Solution

Derivation of the equation by the calculus method:-
we know that,
Acceleration, a=$$\frac{dv}{dt}$$
or, $$\int_{v}^{u} 1dv=\int_{a}^{0} 1dt$$
or, $$V-u=at$$
or,v=$$u+at$$
$$-2$$
      
      $$a=\frac{VdV}{ds}$$
      $$a=\frac{Vdv}{ds}$$
or,   $$\int_{v}^{u} VdV=\int_{s}^{0}$$ ads
or,   $$\frac({v^2}{2})_u^v=as$$
or,   $$v^2-u^2=2as$$
$$3-$$

  putting v=$$u+at$$ in equation 
            $$V^2-u^2$$,
  $$(u+at^2)^2-u^2=2as$$
or, $$2uat+a^2t^2=2as$$
or, $$s=ut+\frac{1}{2}at^2$$

Physics

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