Question

.prove : s=ut +½ at²​

Answer 1

Step-by-step explanation:

Let the distance covered by the body be s, initial and final velocities be u and v respectively and time taken be t.

`\therefore Average\: velocity = (u+v)/(2) \\\\</p><p>Now, \:we \:know\: that\\\\</p><p>Distance \:covered\\ = Average\: velocity * time\\\\</p><p>\therefore s= ((u+v) )/(2) * t..... (1)\\\\`

By first equation of motion:

`v = u + at`

Substituting the value of v in equation (1), we find:

`s= ((u+u + at))/(2) * t\\\\</p><p>\therefore s= ((2u + at))/(2) * t\\\\</p><p>\therefore s= ((2ut + at^2))/(2)\\\\</p><p>\therefore s= \frac{2ut} {2}+ (at^2)/(2)\\\\ </p><p> \huge \orange {\boxed {\therefore s= ut+ (1)/(2)at^2}} \\\\`

Hence proved.