Question

derive equations by analytical method.1- s=ut+1/2 a²​

Answer 1

Wkt that distance travelled by a particle in a given time interval = area under velocity - time graph

=

$\frac{1}{2} \times sum \: of \: parallel \: side \times perpendicular \: distancebetween \: the \: parallel \: side \\ \\ oa = u \\ bd = v \\ = \frac{1}{2} \times (u + v) \times (t) \\ = \frac{1}{2} \times (u + u + at) \times t \\ = \frac{1}{2} \times (2u + at) \times t \\ = \frac{1}{2} \times 2(u + \frac{at}{2} \times t \\ s = u + \frac{1}{2} {at}^{2}$