Question

prove graphically S is equal to UT plus half at square

Answer 1

$\textbf{Heya}$

Area under the v-t graph represents displacement, s covered by the body.

Displacement = Area of the figure OABCD

s = Area of triangle ∆ ABC + Area of rectangle OACD

s = 1/2 × AC × BC + OA × OD

s = 1/2 × t × (v - u) + u × t

Using 1st equation of motion, we get

v - u = at .........(1)

s = 1/2 × t × (at) + u × t

s = 1/2 × at^2 + ut

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

$\textbf{Hope this helps you}$