Section 4.2: Acceleration Vector

Acceleration vector

The instantaneous acceleration found by taking the derivative of the velocity function with respect to time in unit vector notation

Velocity function

A vector function that describes the rate of change of position with respect to time, usually expressed in unit vector notation

Position function

A vector function that describes the location of an object as a function of time, usually expressed in unit vector notation

Constant acceleration

A situation where the acceleration vector remains constant over time, allowing the use of simplified kinematic equations

Kinematic equations in three dimensions

Equations that describe motion with constant acceleration along each axis (x, y, and z) independently

Unit vector notation

A way of expressing vectors using i, j, and k unit vectors for the x, y, and z directions respectively

Acceleration components

The individual x, y, and z components of the acceleration vector, found by taking the second derivative of the respective position components

Velocity components

The individual x, y, and z components of the velocity vector, found by taking the first derivative of the respective position components

Second derivative of position

The acceleration vector can be expressed as the second derivative of the position function with respect to time

Three-dimensional motion analysis

The process of solving problems involving motion in three dimensions by applying one-dimensional motion equations along perpendicular axes