Question

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

Answer 1

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

$V^2-u^2$,

$(u+a{t}^2{)}^2-u^2=2as$

or, $2uat+a^2{t}^2=2as$

or, $s=ut+\frac{1}{2}a{t}^2$