Motion Along a Straight Line

Vocabulary-style flashcards covering the fundamental concepts of 1D kinematics, including speed, velocity, acceleration, graph interpretation, calculus applications, and UAM equations.

Vectors

Measurements that include both size (Magnitude) and direction.

Scalars

Measurements that include size (Magnitude) but do not have a direction.

Distance ($d$)

A scalar quantity that describes how far something moves total.

Displacement ($\Delta x$)

A vector quantity that describes how far something moves from its starting point; the change in position.

Speed

A scalar quantity describing how fast something moves; it is always positive or zero.

Velocity ($v$)

A vector quantity describing how fast position changes; it can be positive or negative.

Average Velocity ($v_{avg}$)

Velocity measured between two points (initial and final), calculated as $v_{avg} = \frac{\Delta x}{\Delta t}$.

Acceleration ($a$)

A vector quantity describing how fast velocity changes, with units of $m/s^2$.

Position-time Graph Slope

Represents the velocity ($v$) of the object.

Position-time Graph Curvature

Indicates acceleration; curving upward (smiley) indicates positive acceleration, while curving downward (frowny) indicates negative acceleration.

Instantaneous Velocity

The velocity of an object at one specific point (instant) in time, determined by the slope of the tangent line on a position-time graph.

Velocity-time Graph Slope

Represents the acceleration ($a$) of the object.

Velocity-time Graph Area

Represents the displacement ($\Delta x$) of the object, also known as the area "under the curve."

Acceleration-time Graph Area

Represents the change in velocity ($\Delta v$) of the object.

Position Function ($x(t)$)

An equation that gives an object's position for any value of time ($t$).

Derivative of Position

The mathematical operation performed on a position function $x(t)$ to obtain the instantaneous velocity function $v(t)$.

Integral of Velocity

The mathematical operation performed on a velocity function $v(t)$ to calculate displacement (without $+C$) or the position function (with $+C$).

Uniformly Accelerated Motion (UAM)

Motion where acceleration is constant, allowing for the use of the four Equations of Motion.

Ignored Variable

In UAM problems, the variable among the five ($\Delta x$, $v_0$, $v$, $a$, $t$) that is neither asked for nor given in the problem text.

Free Fall

Motion where the only force acting on an object is gravity ($F_G$).

Acceleration due to gravity ($g$)

The constant acceleration experienced by objects in free fall on Earth, which is always $9.8\,m/s^2$ regardless of weight.

Overtake/Catch up Condition

The point where two separate objects share the same position at the same time ($x_A = x_B$).