Question

For a constant acceleration, what is the nature of the velocity time graph

Answer 1

We have to draw the velocity time graph for constant acceleration of an object .

Let's assume that the acceleration is constant and equal to k units.

So the acceleration time graph will be a straight line parallel to the time axis. This represents a motion with constant acceleration.

Now , using calculus , we can say :

$\therefore \: \dfrac{dv}{dt} = k$

$= > dv = k \: dt$

Integrating on both sides, we get :

$\displaystyle \: = > \int \: dv = k \: \int \: dt$

$= > v = kt \: + c$

c is a constant for indefinite integral.

So as the form of Y = mX + c , we can say that the velocity vs time graph will be linear .

Refer to the attached photo to understand better.