Question

V ² - u 2 +2as graph method

Answer 1

Displacement = area under the velocity time graph

s = area of trapezium ACEF

s = 1/2 ( b¹ + b² ) h

⇒s = 1/2 ( AF+CE )FE

⇒s = 1/2 ( u + v) t               ...(i)

We know,  v= u+ at

⇒t = (v - u)/a

Now putting this value of t in eq.(i) :-

s = 1/2( v+u) (v-u)

⇒s = 1/2a[( v + u) (v - u)]

⇒2as = (v + u)(v - u)

⇒2as = v² - u²

⇒v² - u² = 2as

PROVED !!