Course Title: Dynamics of a Particle
Course Code: DYN 233
Rectilinear Kinematics: Erratic Motion
Objectives
1. Define and interpret position, velocity, and acceleration in rectilinear motion.
2. Distinguish between average and instantaneous kinematic quantities.
3. Construct velocity and acceleration graphs from a given position–time graph using slope
relationships.
4. Construct position and velocity graphs from velocity–time and acceleration–time graphs using area
relationships.
5. Analyze erratic motion problems using graphical data to determine time, displacement, velocity, and
acceleration.
2 Introduction
In the previous discussion, rectilinear motion was analyzed assuming continuous, well-defined
functions of position, velocity, and acceleration. In many practical situations, however, a particle’s motion
does not follow simple continuous relations, and its behavior must instead be examined using graphical and
experimental data.
2.1 RECTILINEAR KINEMATICS: ERRATIC MOTION
When a particle’s motion during a time is erratic, it may be difficult to obtain a continuous function
to describe its position, velocity, or acceleration. Instead, the motion may best be described graphically
using a series of curves that can be generated experimentally by computer. There are several frequently
occurring situations:
• Given 𝑠 − 𝑡 Graph, Construct 𝑣 − 𝑡 Graph. If the position of a particle can be plotted over
time (𝑠 − 𝑡 graph), the particle’s velocity as a function of time (𝑣 − 𝑡 graph) can be obtained
by measuring the slope of the 𝑠 − 𝑡 graph.
© 2026 Prepared by ENGORA—the library of engineering notes. Redistribution, reuploading, resale, or public
posting without permission is not allowed. For more of these, contact: stuvia
, 𝑑𝑠
=𝑣
𝑑𝑡
slope of 𝑠 − 𝑡 graph = 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦
• Given 𝑣 − 𝑡 Graph, Construct 𝑎 − 𝑡 Graph. When the particle’s 𝑣 − 𝑡 graph is known, the
particle’s acceleration as a function of time (𝑎 − 𝑡 graph) can be obtained by measuring the
slope of the 𝑣 − 𝑡 graph.
𝑑𝑣
=𝑎
𝑑𝑡
slope of 𝑣 − 𝑡 graph = 𝑎𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛
• Given 𝑎 − 𝑡 Graph, Construct 𝑣 − 𝑡 Graph. When the particle’s 𝑎 − 𝑡 graph is given, the
𝑣 − 𝑡 graph may be constructed by:
© 2026 Prepared by ENGORA—the library of engineering notes. Redistribution, reuploading, resale, or public
posting without permission is not allowed. For more of these, contact: stuvia
Course Code: DYN 233
Rectilinear Kinematics: Erratic Motion
Objectives
1. Define and interpret position, velocity, and acceleration in rectilinear motion.
2. Distinguish between average and instantaneous kinematic quantities.
3. Construct velocity and acceleration graphs from a given position–time graph using slope
relationships.
4. Construct position and velocity graphs from velocity–time and acceleration–time graphs using area
relationships.
5. Analyze erratic motion problems using graphical data to determine time, displacement, velocity, and
acceleration.
2 Introduction
In the previous discussion, rectilinear motion was analyzed assuming continuous, well-defined
functions of position, velocity, and acceleration. In many practical situations, however, a particle’s motion
does not follow simple continuous relations, and its behavior must instead be examined using graphical and
experimental data.
2.1 RECTILINEAR KINEMATICS: ERRATIC MOTION
When a particle’s motion during a time is erratic, it may be difficult to obtain a continuous function
to describe its position, velocity, or acceleration. Instead, the motion may best be described graphically
using a series of curves that can be generated experimentally by computer. There are several frequently
occurring situations:
• Given 𝑠 − 𝑡 Graph, Construct 𝑣 − 𝑡 Graph. If the position of a particle can be plotted over
time (𝑠 − 𝑡 graph), the particle’s velocity as a function of time (𝑣 − 𝑡 graph) can be obtained
by measuring the slope of the 𝑠 − 𝑡 graph.
© 2026 Prepared by ENGORA—the library of engineering notes. Redistribution, reuploading, resale, or public
posting without permission is not allowed. For more of these, contact: stuvia
, 𝑑𝑠
=𝑣
𝑑𝑡
slope of 𝑠 − 𝑡 graph = 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦
• Given 𝑣 − 𝑡 Graph, Construct 𝑎 − 𝑡 Graph. When the particle’s 𝑣 − 𝑡 graph is known, the
particle’s acceleration as a function of time (𝑎 − 𝑡 graph) can be obtained by measuring the
slope of the 𝑣 − 𝑡 graph.
𝑑𝑣
=𝑎
𝑑𝑡
slope of 𝑣 − 𝑡 graph = 𝑎𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛
• Given 𝑎 − 𝑡 Graph, Construct 𝑣 − 𝑡 Graph. When the particle’s 𝑎 − 𝑡 graph is given, the
𝑣 − 𝑡 graph may be constructed by:
© 2026 Prepared by ENGORA—the library of engineering notes. Redistribution, reuploading, resale, or public
posting without permission is not allowed. For more of these, contact: stuvia
