Lesson 11: Summary on Graphical Representation of Uniformly Accelerated Motion in 1D
- Graphs are pictorial representations of data, explaining the relationship between dependent and independent variables.
- The independent variable is typically represented on the x-axis, while the dependent variable is on the y-axis.
- A displacement-time graph, also known as a position-time graph, depicts how far an object is from its initial point over time.
- In uniform motion, where an object moves in a straight line at a constant speed, the displacement-time graph is a straight line with a non-zero slope.
- The slope indicates the object’s constant velocity.
- Acceleration, the rate of change of velocity, is depicted differently:
- a graph of uniform acceleration shows a curved line because velocity changes at a constant rate.
- If the curve’s slope increases, it signifies positive acceleration;
- if it decreases, it indicates deceleration. Understanding these graphs involves interpreting the slope: a flat line means the object is at rest, an upward straight line indicates constant speed, and a curved line shows acceleration or deceleration based on the slope’s behavior.
- Interpreting displacement-time graphs helps to understand an object’s motion: a flat slope indicates no motion, a constant positive slope shows steady motion, and a curve reflects changing speeds.
- The area under these graphs represents the displacement from the starting position. For velocity-time graphs, the y-axis represents velocity, the x-axis represents time, and the slope represents acceleration. The first equation of motion, v=u+atv = u + atv=u+at, is represented in these graphs, indicating how velocity changes over time.
- The area under the velocity-time graph provides the displacement.
- In an acceleration-time graph, where acceleration is plotted against time, a constant acceleration results in a horizontal line parallel to the time axis.
- This graphical representation helps visualize how acceleration, velocity, and displacement interrelate, providing a comprehensive understanding of an object’s motion.