Kinematics: Motion in One and Two Dimensions - Physics (Undergraduate Foundation)

Motion is the most fundamental concept in physics. This course provides the mathematical framework to describe it with quantitative precision. We will systematically analyse motion in one, two, and three dimensions, progressing from motion along a straight line to the vector analysis of projectiles and general spatial motion. This requires a full command of both vector algebra and introductory calculus. The principles of kinematics are the bedrock of physical analysis, engineering design, and biomechanics. This knowledge is required to analyse everything from vehicle performance and projectile trajectories to the movement of organisms and robotic motion. A command of this material is essential for any work involving the dynamics of moving systems, providing the tools to predict and control motion in the real world. Upon completion, you will be able to analyse motion in multiple dimensions. You will solve one-dimensional problems using the standard kinematic equations for constant acceleration. You will analyse two-dimensional projectile motion by resolving vectors into independent components. Critically, you will use vector calculus to describe the general case of motion with variable acceleration. This course is designed for first-year university students of the physical, biological, and medical sciences, as well as engineering and computer science. A firm command of vector algebra and introductory calculus (differentiation and integration) is a mandatory prerequisite. This material is the necessary foundation for the subsequent study of Newtonian dynamics and biomechanics.

19 hrs

Enrolment valid for 12 months

This course is also part of the following learning track. You may join the track to gain comprehensive knowledge across related courses.

PHY 101: General Physics I - Mechanics

This learning track provides a complete and rigorous treatment of introductory classical mechanics as specified by the NUC Core Curriculum. It is structured to build a comprehensive analytical framework, starting with the mathematical description of motion (kinematics) and progressing through its causes (Newtonian dynamics), the powerful conservation laws, the dynamics of rotating systems, and finally, the principles of universal gravitation. Mastery of this material is the non-negotiable foundation for all subsequent study in physics and engineering. The principles of classical mechanics are the operational language for analysing the physical world. This track provides the essential toolset for solving problems in every field of engineering, from aerospace to civil, and for understanding phenomena from the trajectory of a projectile to the orbits of planets. By the end of this track, you will be able to analyse motion using vectors and calculus, apply Newton's laws to solve any standard dynamics problem, use conservation laws to analyse complex systems and collisions, analyse rotational motion, and solve problems in celestial mechanics. This learning track is a mandatory prerequisite for all first-year university students of physics, engineering, and related physical sciences. It provides the foundational knowledge required for all subsequent courses in mechanics, electromagnetism, thermodynamics, and modern physics.

Course Chapters

1. Introduction

This chapter establishes the rigorous language of kinematics. It defines the core quantities of motion – displacement, velocity, and acceleration – with a critical focus on the distinction between their scalar and vector forms. This foundation is the prerequisite for all subsequent analysis. Key objectives: distinguish between scalar and vector quantities; define average and instantaneous acceleration; and use differentiation to relate displacement, velocity, and acceleration.

Concept Overviews

5 Lessons

1:20:16

2. Motion in One Dimension

This chapter applies kinematic principles to the simplest case: motion along a straight line. We will cover motion with variable acceleration using calculus, and then focus on the critical case of constant acceleration and its set of standard equations. Mastery of 1D motion is the required foundation for all further analysis. Key objectives: use calculus to relate displacement, velocity, and acceleration; apply the kinematic equations to solve constant acceleration problems; and analyse vertical motion under gravity.

Concept Overviews

4 Lessons

1:48:13

Problem Walkthroughs

6 Lessons

1:23:22

3. Motion in Two or Three Dimensions

This chapter extends kinematic analysis to two and three dimensions. It establishes the general vector framework and calculus-based methods required to describe motion in a plane and in space. This mathematical toolkit is the direct prerequisite for analysing specific cases like projectile motion. Key objectives: describe position, velocity, and acceleration using standard vector notation; and apply differentiation and integration to these vectors to analyse motion with variable acceleration.

Concept Overviews

3 Lessons

58:29

Problem Walkthroughs

8 Lessons

1:58:28

4. Projectile Motion

This chapter provides a complete analysis of projectile motion, the primary application of two-dimensional kinematics. The core principle is the complete independence of horizontal motion (at constant velocity) and vertical motion (at constant acceleration). Key objectives: apply the principle of independent components to projectile problems; derive and use the equations for range, maximum height, and time of flight; and solve projectile trajectory problems.

Concept Overviews

5 Lessons

1:46:02

Problem Walkthroughs

6 Lessons

2:01:58

5. Uniform Circular Motion

This chapter examines uniform circular motion, a special case of two-dimensional motion where an object's speed is constant but its velocity is not. We will introduce the concept of an acceleration that serves only to change the direction of the velocity vector. Key objectives: define the descriptive quantities of circular motion (period, speed); explain the nature and direction of centripetal acceleration; and apply its formula to solve problems.

Concept Overviews

3 Lessons

1:27:21

Problem Walkthroughs

5 Lessons

42:16

6. Relative Motion

This chapter introduces the vector framework required to relate motion across different inertial frames of reference. Mastering these transformations is critical for solving complex real-world navigation and tracking problems where both the object and the observer are in motion. You will master four key objectives: applying the subscript notation for relative velocity; calculating resultant velocities in one dimension; resolving perpendicular vector components in two dimensions; and determining optimal headings for aircraft and maritime transit.

Concept Overviews

1 Lesson

27:22

Problem Walkthroughs

4 Lessons

1:25:30

7. Conclusion

This chapter consolidates the core concepts of kinematics. It provides a structured summary of the mathematical tools and physical principles used to describe motion, reinforcing the foundation for the study of dynamics. The conclusion summarises the key definitions and equations. It also provides a forward look to the next course, where Newton's laws will be used to explain the causes of motion.

Concept Overviews

1 Lesson

9:46