Describing Motion Chapter 3

What is a motion diagram? A Motion diagram is a useful tool to study the relative motion of objects. From motion diagrams, it is possible to observe an object under: Constant velocity Accelerating positively Accelerating negatively Or Stationary

Motion Diagrams Constant Speed: Positive Acceleration: Negative Acceleration:

The Particle Model To simplify motion diagrams, we can concentrate all the motion through a single point at or near the center of gravity.

The Particle Model Constant Speed: Fast Positive Acceleration: Fast Negative Acceleration:

The Particle Model Constant Speed: Slow Positive Acceleration: Slow Negative Acceleration:

Determining Motion An object’s motion can be determined if its initial and subsequent positions are identified relative to time. Initial Time = ti Initial Position = di Initial Velocity = vi Final Time = tf Final Position = df Final Velocity = vf

Average Velocity The average velocity is the ratio of displacement and time as follows: Where: Dd = the displacement vector Dt = change in time ti and di represent the starting position tf and df represent the final position Average velocity does not tell you how the velocity varied during the time interval between the points, di and df. v = = Dd Dt df - di tf - ti (1)

Graphical Representation of Velocity A graph of an object moving at constant velocity will consist of a straight line. The slope of this line will equal the average velocity of the object.

Average Acceleration An object in motion with changing velocity is under acceleration Acceleration is the rate of change of velocity as follows: As with average velocity, the average acceleration does not tell you how it varied during the time interval ti to tf. a = = Dv Dt vf - vi tf - ti (2)

Graphical Representation of Average Acceleration A graph of an object moving at constant acceleration will consist of a straight line. The slope of this line will equal the average acceleration of the object. The average between the initial and final values for velocity will equal the average. vi vf vavg