Kinematics: Acceleration and Displacement

Vocabulary flashcards covering velocity, acceleration, displacement, kinematics equations, and graph interpretations based on the lecture material.

Acceleration

A vector quantity defined as the rate at which an object's velocity changes over time.

Average Acceleration

The change in velocity ($\Delta v$) divided by the time interval ($\Delta t$), defined mathematically as $\frac{v_2 - v_1}{t_2 - t_1}$ with units of meters per second squared ($m/s^2$).

Instantaneous Acceleration

The limit of the change in velocity as the time interval approaches zero.

Constant Acceleration

A condition where an object's acceleration does not change over time, producing an acceleration-time graph with a zero slope and making instantaneous acceleration equal to average acceleration.

Little $g$

The constant gravitational acceleration for objects near the Earth's surface, featured in the force equation $F = mg$.

Kinematics Equation 1

An equation showing how velocity changes as a function of time under constant acceleration, written as $v_x = v_{0x} + a_x t$.

Speeding Up (Motion Rule)

Occurs whenever an object's velocity vector and acceleration vector point in the same direction (both positive or both negative).

Slowing Down (Motion Rule)

Occurs whenever an object's velocity vector and acceleration vector point in opposite directions.

Velocity-Time Graph Slope

A graph where the slope of a line connecting two points represents average acceleration, and the slope of the tangent line at a single point represents instantaneous acceleration.

Average Velocity (General Definition)

An object's displacement ($\Delta x$) divided by the elapsed time ($\Delta t$), expressed as $\bar{v} = \frac{\Delta x}{\Delta t}$, which is true for both constant and non-constant acceleration.

Average Velocity (Constant Acceleration Definition)

The average of an object's initial velocity ($v_0$) and final velocity ($v$), calculated as $\bar{v} = \frac{v + v_0}{2}$, which applies only when acceleration is constant.

Displacement Equation (Combined Kinematics)

An equation derived by combining average velocity expressions to find displacement directly, expressed as $\Delta x = \frac{v + v_0}{2} t$.

"From Rest"

A phrase in physics problems indicating that the initial velocity ($v_0$) of an object is $0\,m/s$.

"Bring to a Stop"

A phrase in physics problems indicating that the final velocity ($v$) of an object is $0\,m/s$.