Velocity-Time Graph-I

Mother Nature has blessed us with different types of scenic beauties like Mountains, Waterfalls etc.

The fast flowing of water in a waterfall looks so fascinating

The largest waterfall in the world is the Victoria Falls

The physical quantity which determines how fast the water flows is known as Speed

When we consider speed along with direction it is known as Velocity

Mathematically,$\text{Velocity}=\frac{\text{ Displacement }}{\text{ Time }}$ where Displacement is the change in object's position considering its initial and final position

That means Velocity, Time and Displacement are inter related to one another

Let us consider an object which is moving with different velocities at different times.

Now let us put the values of Velocities and intervals of time in a graph where Velocity is plotted along y-axis and time is plotted along the x-axis

Now, assuming that the velocity of the object is 0 m/s at time t=0s and then it increases to $v_1$ in time $t_1$

Again, the velocity of the object decreases in the negative direction at the time $t_2$

Then, the object acquired a negative velocity${-v}_2$ at time $t_3$

The negative velocity of the object remains constant for some time and at $t_4$, it attains a zero velocity

We know that the value of Velocity and Time will help us to find the Displacement of the object

The Displacement of the object can be obtained from the previous Velocity-Time graph

It is obtained by calculating the area of the curve under Velocity- Time graph i.e area enclosed by the time axis and the curve

Therefore, total Displacement of the body from 0s to $t_4$s will the area of the triangle OAB and trapezoid BCDE

i.e. Total Displacement= Area of OAB + Area of BCDE

Revision

Velocity is plotted against time in a graph known as Velocity-Time Graph to obtain the Displacement of the body

The total Displacement of the body from the graph is obtained by calculating the area enclosed by the curve in the graph

The End