Question

Using velocity time graph derive
S = ut+1/2at^2

Answer 1

Answer:

Let us consider a velocity time graph in which Velocity increases linearly from initial velocity u to final velocity v

So , Displacement can be found out by calculation of area under velocity-time graph.

Let Displacement be s

Displacement = Area of trapezium

$= > s = \dfrac{1}{2} \{u + v \} \times t$

$= > s = \dfrac{1}{2} \{u + (u + at) \} \times t$

$= > s = \dfrac{1}{2} \{2u + at \} \times t$

$= > s = \dfrac{1}{2} (2ut + a {t}^{2} )$

$= > s = ut + \dfrac{1}{2} a {t}^{2}$

[ Hence proved ]