Notes on Delta Notation, Displacement, and 1D Kinematics

Delta notation

• $\Delta t$ = change in time
• $\Delta x$ = change in position (displacement)
• The symbol $\Delta$ denotes a change

Displacement and arrows

• Displacement is a vector equal to the change in position
• Visualized as arrows showing a start and end position
• In 1D, displacement lies along the $x$ axis

1D coordinate system basics

• Origin is the reference point
• The $x$-axis defines the horizontal coordinate
• Sign of displacement depends on direction along $x$

Time steps / video frames

• Frames captured in sequence separated by $\Delta t$
• Smaller $\Delta t$ yields smoother motion

Velocity (basic relation)

• Average velocity: $v = \frac{\Delta x}{\Delta t}$
• As $\Delta t$ becomes very small, this approaches instantaneous velocity

Observation context

• Observing moving objects (e.g., Jupiter’s position over time) illustrates displacement with arrows
• Helps connect time, position, and motion concepts