Equation of Motion from Graph

Understanding the Graph:
- First, analyze the given graph which shows the position of an object as a function of time.
- The graph consists of two distinct sections - a straight line and a curve.

Interpreting the Straight Line:
- The straight line represents uniform motion where the object covers equal distances in equal intervals of time.
- The slope of the line determines the velocity of the object. A steeper slope indicates a higher velocity.

Interpreting the Curve:
- The curved part of the graph indicates accelerated motion.
- The curvature of the graph represents the acceleration of the object. A sharper curve indicates higher acceleration.

Deriving the Equation of Motion:
- To derive the equation of motion, we need to find the mathematical relationship between position, velocity, and acceleration.
- For the straight line portion, the equation is given by: position = initial position + velocity * time
- For the curved portion, the equation is given by: position = initial position + initial velocity * time + (1/2) * acceleration * time^2

Combining the Equations:
- By combining the equations for both sections of the graph, we can derive the complete equation of motion for the object.
- This equation will include terms for initial position, initial velocity, acceleration, and time.

Conclusion:
- By analyzing the graph and understanding the concepts of uniform and accelerated motion, we can derive the equation of motion for an object based on its position-time graph.