Mastering Kinematics: The Science of One-Dimensional Motion

Scalars

Quantities fully described by a magnitude only.

Vectors

Quantities fully described by both magnitude and direction.

Kinematics

The description of motion.

Distance

A scalar representing the total length of the path traveled.

Displacement

A vector representing the straight-line change in position.

Average Speed

The total distance traveled divided by the total time elapsed.

Average Velocity

The displacement divided by the time interval.

Acceleration

The rate of change of velocity.

Position ($x$)

The specific location of an object relative to a defined origin.

Positive Direction

Usually implies right, up, east, or forward.

Negative Direction

Usually implies left, down, west, or backward.

Motion Diagram

Visualizes the position of an object at equal time intervals.

Position-Time Graph

Graph showing position versus time; slope represents velocity.

Velocity-Time Graph

Graph showing velocity versus time; slope represents acceleration.

Acceleration-Time Graph

Graph showing acceleration versus time; area under the curve represents change in velocity.

Concave Up

Indicates positive acceleration in a Position-Time graph.

Concave Down

Indicates negative acceleration in a Position-Time graph.

UAM

Uniform Accelerated Motion; describes motion with constant acceleration.

Displacement Formula

Δx = xf - xi, where xf is final position and xi is initial position.

Negative Acceleration

Does not always mean slowing down; depends on the velocity's sign.

Average Velocity Formula

v = Δx / Δt.

Final Velocity ($v_x$)

The velocity of an object at the end of a time interval.

Initial Velocity ($v_{x0}$)

The velocity of an object at the beginning of a time interval.

Acts Against Gravity

When an object is thrown up, its acceleration is still down due to gravity.

Elapsed Time

Total time that has elapsed during the motion.

Change in Velocity

Represented by the area under the acceleration-time curve.

Constant Velocity

When dots in a motion diagram are spaced equally apart.

Worked Example Problem

A car traveling at 20 m/s decelerates at -5 m/s² before stopping.