Question

What is $v-t$ graph? Derive $x=v_{0}t=\frac{1}{2}a{t}^2$ using $v-t$ graph.

Answer 1

Graph plotted with time on $x-$axis and velocity on $y$ axis is called $V-t$ graph.

$V-t$ graph of a particle having constant acceleration a distance travelled by particle is area under $(V-t)$ graph.

$\Rightarrow x=\frac{1}{2}\times t\times \frac{\Delta V}{\Delta t}=\frac{1}{2}t.a=\frac{1}{2}{at}^2=x$

$V-t$ graph of a particle having a acceleration distance travelled by particle in time $t$.

$x=V_{0}t$ (Area under $(V-t)$ graph).