Graphical Derivation of First Equation of Motion
The first equation of motion can be derived graphically by analyzing the velocity-time graph of an object in motion.

Key Steps:
- Start by plotting a velocity-time graph with time on the x-axis and velocity on the y-axis.
- The slope of the graph represents the acceleration of the object.
- The area under the graph represents the displacement of the object.

Explanation:
- Initially, the object is at rest with a velocity of 0 m/s.
- As time progresses, the velocity of the object increases linearly with time, indicating a constant acceleration.
- The slope of the graph gives the acceleration, which is constant in this case.
- The equation of motion can be derived from the slope of the graph, which gives the acceleration as a function of time.
By analyzing the velocity-time graph, we can derive the first equation of motion which relates initial velocity, acceleration, time, and displacement of an object in motion. This graphical derivation provides a visual representation of the relationship between velocity, time, and displacement, helping us understand the motion of objects more intuitively.