Question

S=ut+1/2at2 prove by graphical method.

Answer 1

See the image attached.
The total area enclosed by the straight line is displacement (S)
Area = ut + 0.5(v-u)t
We know that a = (v - u)/t
Therefore,
Area = ut + 0.5at^2

Answer 2

To prove : Second equation of motion

Explanation:

let

u = initial velocity

v = final velocity

a = acceleration

then

second equation of motion is

let the time be t and the distance covered be s

thus

area of trapezium ABODE

= area of triagle ABD + area of rectangle AODE

$s = \frac{1}{2}\times AB \times AD + (OD\times OE)\\\\s = \frac{1}{2}\times DC \times AD+ (u+t)\\\\s = \frac{1}{2}\times at+t+ ut\\\\thus\\\\s = ut+ \frac{1}{2}at^2$

hence proved