Graph v-t Area in Velocity time Graph

Description:

Area enclosed between the x-axis i.e. time and the velocity graph is known as area below the graph.

Area covered by the graph within the time t₁ and  t₂ is calculated as −

From figure −

Area = BC × DC

As BC = Velocity and DC = time

Area = Velocity × time

Area = displacement

Area under v-t graph gives displacement.

Hence, velocity-time graph is capable of showing the relation between all the four quantities – velocity (y-axis), time (x-axis), acceleration (slope) and displacement (area).

We can derive the kinematic equation

S = ut + 1/2 at²

From v-t graph

Consider the following graph −

Displacement is given by −

Displacement = Area under graph

S = DACO

S = Area(⚀ DBCO + Δ DAB)

S = BC × OC + 1/2 AB × DB

S = BC × OC + 1/2 AB/DB × DB²

Substituting values from figure, we get −

S = u × t + 1/2 a × t²

S = ut + 1/2 at²