Derivation of 3 Equations of Motion by Graphical Method

Introduction:
The three equations of motion are the fundamental equations in physics that describe the motion of an object. They are used to calculate the position, velocity, and acceleration of an object in motion. In this article, we will discuss the derivation of these equations by the graphical method.

Graphical Method:
The graphical method is a simple and easy way to derive the equations of motion. The method involves plotting the motion of an object on a graph and then analyzing the graph to obtain the equations.

Derivation of the First Equation of Motion:
The first equation of motion relates the displacement, initial velocity, final velocity, and time taken by an object in motion. The equation is given as:

s = ut + 1/2 at^2

where s is the displacement, u is the initial velocity, a is the acceleration, and t is the time taken.

To derive this equation by the graphical method, we need to plot a graph of the motion of the object. The x-axis represents time, and the y-axis represents the velocity of the object. We can then calculate the area under the graph to obtain the displacement.

Derivation of the Second Equation of Motion:
The second equation of motion relates the final velocity, initial velocity, acceleration, and displacement of an object in motion. The equation is given as:

v^2 = u^2 + 2as

where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the displacement.

To derive this equation by the graphical method, we need to plot a graph of the motion of the object. The x-axis represents time, and the y-axis represents the velocity of the object. We can then calculate the slope of the graph to obtain the acceleration. We can also calculate the area under the graph to obtain the displacement. We can then substitute these values into the equation to obtain the final velocity.

Derivation of the Third Equation of Motion:
The third equation of motion relates the final velocity, initial velocity, acceleration, and time taken by an object in motion. The equation is given as:

v = u + at

where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time taken.

To derive this equation by the graphical method, we need to plot a graph of the motion of the object. The x-axis represents time, and the y-axis represents the velocity of the object. We can then calculate the slope of the graph to obtain the acceleration. We can also use the initial and final velocities to obtain the change in velocity. We can then substitute these values into the equation to obtain the time taken.

Conclusion:
The graphical method is a simple and easy way to derive the three equations of motion. It involves plotting a graph of the motion of an object and then analyzing the graph to obtain the equations. These equations are fundamental in physics and are used to calculate the motion of objects in various situations.

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