Motion Along a Straight Line - Vocabulary

Vocabulary flashcards covering core definitions, mathematical formulas, and concepts from Chapter 2: Motion Along a Straight Line.

Kinematics

A branch of mechanics that studies the motion of objects without consideration of the forces that cause the motion.

Dynamics

A branch of mechanics that studies why objects move.

1-Dimensional Motion

The motion of an object along a straight line, which can be along a horizontal, vertical, or inclined path.

Position

The location $x$ of a particle on an axis relative to a reference point known as the origin.

Origin

The zero point of an axis that serves as the reference point for defining an object's location.

1D Coordinate System

A straight-line axis with an origin zero point, where the positive direction points toward increasing positive numbers and the negative direction points in the opposite direction.

Positive Direction

The direction along a coordinate axis in which numbers increase positively.

Negative Direction

The direction along a coordinate axis opposite to the positive direction.

Displacement

The change in position of a particle during a time interval, given by $\frac{\Delta x}{1} = x_2 - x_1$.

Average Velocity

The ratio of displacement $\Delta x$ to the time interval $\Delta t$, expressed as $v_{\text{avg}} = \frac{\Delta x}{\Delta t} = \frac{x_2 - x_1}{t_2 - t_1}$.

Graphical Average Velocity

The slope of the straight line connecting two particular points on an $x(t)$ position-time curve corresponding to $(t_1, x_1)$ and $(t_2, x_2)$.

Average Speed

The total distance moved by a particle during a time interval $\Delta t$ divided by that time interval, expressed as $s_{\text{avg}} = \frac{\text{total distance}}{\Delta t}$.

Instantaneous Velocity

The velocity of a particle at a specific instant in time, defined as the derivative of position with respect to time: $v = \lim_{\Delta t \rightarrow 0} \frac{\Delta x}{\Delta t} = \frac{dx}{dt}$.

Speed

The magnitude of instantaneous velocity.

Average Acceleration

The ratio of the change in velocity $\Delta v$ to the time interval $\Delta t$ during which the change occurs, given by $a_{\text{avg}} = \frac{\Delta v}{\Delta t} = \frac{v_2 - v_1}{t_2 - t_1}$.

Instantaneous Acceleration

The rate of change of velocity with respect to time at a specific instant, defined as $a = \frac{dv}{dt} = \frac{d^2 x}{dt^2}$.

Graphical Kinematic Derivatives

The slope of the position-time curve $x(t)$ represents velocity $v(t)$, and the slope of the velocity-time curve $v(t)$ represents acceleration $a(t)$.

Uniformly Accelerated Motion

Motion in which an object experiences constant acceleration, occurring when velocity and acceleration have the same sign and speed increases.

Uniformly Decelerated Motion

Motion in which an object's velocity and acceleration have opposite signs, causing its speed to decrease.

Free-Fall Motion

Motion of an object rising or falling freely near Earth's surface under the sole influence of gravity.

Free-Fall Acceleration

The constant downward acceleration near Earth's surface directed toward Earth's center, denoted by $g$ and approximately equal to $9.8\,\text{m/s}^2$.