What field of study deals with motion using scalar or vector algebra?

Kinematics is the branch of mechanics that focuses specifically on the motion of objects without considering the forces that cause that motion. It utilizes both scalar and vector algebra to describe various aspects of movement, including displacement, velocity, and acceleration. Scalars provide magnitude only (like speed), while vectors incorporate both magnitude and direction (like velocity).

In kinematics, equations and graphs are used to analyze the position of objects over time, allowing for the calculation of different parameters of motion. For instance, the relationships between distance, time, and velocity are examined using both algebraic equations and graphical representations. By relying on scalar and vector quantities, kinematics effectively describes the complex motions that bodies undergo in various contexts, from simple linear movement to more complicated trajectories.

The other fields mentioned—curvilinear translation, projectiles, and acceleration—are more specific aspects of motion that fall under the broader scope of kinematics. While they are concerned with certain types of motion or aspects of acceleration, they do not encompass the entire study of motion as comprehensively as kinematics does. Therefore, kinematics is the correct answer as it covers the general principles of motion using both scalar and vector algebra effectively.