Question

Deduce the following equations of motion:
(i) s = ut +(1/2)at2
(ii) v2= u2+ 2as​

Answer 1

Answer:

(i)second equation:

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

=distance traveled by object=area if OABC [TRAPEZIUM]

=area of OADC (rectangle) + area of triangle ABD

=u×t+1/2×t×(v-u)

=ut×1/2×t×at

therefore,

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

(ii) second equation:

${v}^{2} = {u}^{2} + 2as$

= S=area of trapezium

=(OA+BC)×OC/2

=(u+v)×t/2

=u+v/2 ×v-u/2

=v^2 -u^2/2a

therefore

${v}^{2} = {u}^{2} + 2as$