# Visualizing Velocity And Displacement Graph

We have already seen mathematical approach towards speed, velocity, distance and displacement. But graphs actually give us a better understanding of the motion. From the point of view of physics one should be able to interpret motion by looking at graphs. Here we will be talking mainly about velocity time graph and displacement time graph. Let’s start with Displacement time, suppose we have the following graph. What can we interpret?

We have to analyze the motion we can break the motion in three segments OA, AB and BC. We know mathematically that,

$v$ = $\frac{dx}{dt}$

So we can interpret that slope of displacement time graph gives us velocity. In segment OA slope is positive and decreasing with time. Hence velocity is positive and decreasing with time. Similarly as slope is zero in AB, velocity is zero in this region. In BC, slope is negative and so velocity is also negative. Now can you think of how the graph will look for a body at rest or uniform motion? Also displacement time graph can go below the x-axis unlike distance time graph which cannot go below x-axis as it is always positive. Next we will be talking about velocity time graph. Let’s take the following example:

The next question is what does the slope of a velocity time graph represent?
From mathematical relations we have,

$a$ = $\frac{dv}{dt}$

So we can say slope of the velocity time graph represents acceleration. Using the above approach we can acceleration is positive in OA and CD while it is negative in the region AC. Also the velocity changes direction at B. We also know,

$dx$ = $∫v dt$

Graphically it means area under velocity-time graph represents displacement. In this case
Displacement = Area of ∆OAB – Area of ∆BCD. Also velocity time graph can go below x-axis but not speed time graph because speed is never negative.

So know that we have learnt basic of graphical approach try to plot velocity and displacement time graph for a ball falling freely under gravity. For more visit BYJU’S.

#### Practise This Question

A body moves along the path OABC.
Which of the following statement about it's position-time graph is true?