Question

Derive an expression for the velocity of the particle after time ‘t’ or Derive $v=u+at$ using the v-t graph.

Answer 1

Consider a particle moving along a straight line with a constant acceleration ‘a’. Let u be its initial velocity and v be its velocity after a time t. The velocity-time graph AB of this article is shown in the figure.
Acceleration of the particle is given by the slope of the v-t graph.
From the graph,
slope of the line $AB=\frac{BC}{AC}=\frac{BC}{OD}=\frac{BD-CD}{OD}$
But, BD = v, the final velocity,
OA = u, the initial velocity,
OD = t, the time.
∴ Slope of the graph AB is,
$a=\frac{BD-CD}{OD}$
$=\frac{v-u}{t}$
Thus $a=v-ut$ or $v=u+at.$