Question

derive the formula :-
1. v=u+at
2. s=at+1/2 ut
3. v2-u2=2as
where the symbol have their usual meanings.

Answer 1

u is the initial velocity
v is the final velocity
in the v-t graph

Acceleration = a = Slope
= BC/EB
= v-u/t
=> at = v-u
=> v = u + at..........(i)

Distance = S = Area of tri.EBC + Area of ABEO
= 1/2×EB×BC + AB×OA
= 1/2×t×(v-u) + u×t
= 1/2at² + ut [ from eq.(i)]

Distance = S = Area of trap. ACEO
= 1/2×(EO+AC)×OA
= 1/2×(u+v)×t
= (v+u)(v-u)/2a [from eq.(i)]
=> S = (v²-u²)/2a
=> 2aS = v² - u²

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