Question

What is V-t graph? Derive x=v0t + 1/2at2 using V-t graph.

Pls ans this..

Answer 1

Velocity-Time graph is known as V-T graph.
see the above image for the derivation ..

Answer 2

Velocity-Time graph is a graph between Velocity on Y axis and Time on X axis representing the type of motion followed by an object.

Derivation:

• Consider the following graph where the initial velocity is u and final velocity is v and time taken is t :

Now, DISPLACEMENT is given as area under v-t graph :

$\sf \: x = area \: of \: trapezium$

$\sf \implies \: x = \dfrac{1}{2} (u + v) \times t$

• Now, v can be written as (u + at)

$\sf \implies \: x = \dfrac{1}{2} (u + u + at) \times t$

$\sf \implies \: x = \dfrac{1}{2} (2 u + at) \times t$

$\sf \implies \: x = \dfrac{1}{2} (2 ut + a {t}^{2} )$

$\sf \implies \: x = ut + \dfrac{1}{2} a {t}^{2}$

[Hence proved].