Equations of Motion by Graphical Method

To derive the equations of motion graphically, we use a velocity-time graph.

1. First equation (v = u + at):

The slope of the velocity-time graph represents acceleration (a). The change in velocity (v−u) is equal to the acceleration multiplied by time (a×t); hence, v=u+at.

2. Second equation (s =${\displaystyle ut+\frac{\text{1}}{\text{2}}a{t}^2}$):

The area under the velocity-time graph gives the displacement (s). The displacement is the sum of the area of the rectangle (ut) and the area of the triangle  (${\displaystyle \frac{\text{1}}{\text{2}}a{t}^2}$), giving the formula s=${\displaystyle ut+\frac{\text{1}}{\text{2}}a{t}^2}$.

3. Third equation (v² = u² + 2as):

From the first equation, v=u+at, solve for t and substitute into the displacement equation s=${\displaystyle ut+\frac{\text{1}}{\text{2}}a{t}^2}$. This gives the relation v²=u²+2as