General Physics I - One-Dimensional Motion

Vocabulary practice flashcards covering fundamental 1D kinematics concepts including position, displacement, velocity, acceleration, graph interpretation, and constant acceleration equations.

Position

The location of an object relative to a chosen reference point called the origin.

Origin

A chosen reference point, usually defined as $x = 0$, used to specify an object's location.

Displacement

The change in an object's position, calculated as $Δx = x_f - x_i$, which is a vector quantity containing both magnitude and direction.

Distance

The total path length traveled by an object, which is a scalar quantity and always zero or positive.

Position–Time Graph

A graph plotting position $x$ on the vertical axis against time $t$ on the horizontal axis to describe motion.

Average Velocity

An object's displacement divided by the elapsed time ($v_{\text{avg}} = \frac{\Delta x}{\Delta t}$), corresponding to the slope of a secant line on a position–time graph.

Average Speed

The total distance traveled divided by the total elapsed time interval ($S_{\text{avg}} = \frac{\text{total distance}}{\Delta t}$).

Instantaneous Velocity

The velocity of an object at a specific instant in time, defined as $v = \lim_{\Delta t \to 0} \frac{\Delta x}{\Delta t} = \frac{dx}{dt}$, corresponding to the slope of the tangent line on a position–time graph.

Acceleration

The rate of change of velocity with time, occurring whenever an object speeds up, slows down, or changes direction.

Average Acceleration

The change in velocity divided by the elapsed time interval ($a_{\text{avg}} = \frac{\Delta v}{\Delta t} = \frac{v_2 - v_1}{t_2 - t_1}$).

Instantaneous Acceleration

The rate of change of velocity at a specific instant in time, defined as $a = \lim_{\Delta t \to 0} \frac{\Delta v}{\Delta t} = \frac{dv}{dt}$, corresponding to the slope of the tangent line on a velocity–time graph.

Speeding Up Condition

A state of motion where velocity $v_x$ and acceleration $a_x$ have the same sign (both positive or both negative).

Slowing Down Condition

A state of motion where velocity $v_x$ and acceleration $a_x$ have opposite signs (one positive and one negative).

Constant Acceleration

Motion in which an object's velocity changes by equal amounts in equal time intervals ($a_x = \text{constant}$).

First Equation of Motion

The kinematic equation for constant acceleration relating final velocity, initial velocity, acceleration, and time: $v_x = v_{0x} + a_x t$.

Second Equation of Motion

The kinematic equation for constant acceleration relating final position, initial position, initial velocity, acceleration, and time: $x = x_0 + v_{0x} t + \frac{1}{2} a_x t^2$.

Fourth Equation of Motion (Time-Independent)

The kinematic equation for constant acceleration relating final velocity, initial velocity, acceleration, and displacement without explicit time: $v_x^2 = v_{0x}^2 + 2 a_x (x - x_0)$.

Area Under a Velocity–Time Graph

The total area bounded by a velocity curve and the time axis, which equals the displacement ($\Delta x$) of the object.

Motion Diagram for Constant Positive Acceleration

A representation showing velocity vectors $\vec{v}$ that lengthen over time to the right while constant acceleration vectors $\vec{a}$ remain equal in length.

Average Velocity Signs on Position–Time Graphs

Graphs demonstrating that $v_{\text{avg}} > 0$ when position increases, $v_{\text{avg}} < 0$ when position decreases, and $v_{\text{avg}} = 0$ when there is no net change in position.