Question

Which part of the velocity time-graph signifies the distance covered by a body?

Answer 1

Hint:Learn the concept of velocity of a body, the acceleration and other different aspects of motion of a body. The velocity of a body is defined by the displacement covered by the body per unit time.

Formula used:
The instantaneous velocity of a body is given by the
\[v = \dfrac{{ds}}{{dt}}\]
where \[v\] is the velocity of the body, \[ds\] is the infinitesimal displacement of the body covered in infinitesimal time \[dt\].
The instantaneous acceleration of the body is given by,
\[a = \dfrac{{dv}}{{dt}}\]
where \[a\] is the acceleration of the body, \[dv\] is the infinitesimal velocity of the body in infinitesimal time \[dt\].

Complete step by step answer:
We know that the velocity of a body is the rate of change of displacement of the body per unit time. Now, when we draw a velocity time graph we plot the velocity along Y-axis and the time along X-axis. So, the slope of the curve is acceleration of the body at a given time. Now, that we can write as, instantaneous acceleration of the body,
\[a = \dfrac{{dv}}{{dt}}\]
Now, we know that, instantaneous velocity of a body is given by the
\[v = \dfrac{{ds}}{{dt}}\]
Now, if we integrate the equation simply we can have, \[s = \int {vdt} \] which is the distance covered by the body.

Now this integration is nothing but the area under the curve since if we simply multiply the length and breadth of a rectangle we get the area of the rectangle. Here the length is the velocity and the breadth is the time.

So, in a velocity time graph the area under the curve represents the distance covered by the body.

Note: In thermodynamics the area under the curve of the P-V curve signifies work done, which is a scalar quantity or in force displacement curve the area under the curve is also work done. In the velocity time graph the area under the curve represents a vector quantity.