Kinematics and Calculus practice flashcards

This set of vocabulary flashcards summarizes key kinematic definitions and calculus concepts including displacement, velocity, acceleration, differentiation rules, and integration principles found in the lecture notes.

Reference frame

A set of coordinate axis with respect to which we measure the position of any particle.

Motion

Occurs when a particle's position vector changes within a certain reference frame.

Displacement ($S$)

The change in position vector, mathematically defined as $S = \text{r}_f - \text{r}_i$.

Distance ($l$)

The length of the path in moving from one point to another; it is always greater than or equal to the magnitude of displacement.

Average Velocity ($V_{\text{avg}}$)$$

The ratio of displacement during a time interval to the duration of that time interval ($V_{\text{avg}} = \frac{\triangle S}{\triangle t}$).

Differentiation ($\frac{dx}{dt}$)

The derivative of $x$ with respect to $t$, representing the instantaneous rate of change or the slope of the $x-t$ graph.

Extrema

The collective name for maxima and minima points where the derivative of a function is equated to zero ($\frac{dy}{dt} = 0$).

Second Derivative

The derivative of a derivative ($\frac{d^2y}{dt^2}$), used to differentiate between maxima (negative value) and minima (positive value).

Integration

The reverse process of differentiation (Anti-Derivatives), physically representing the summation of infinitesimal parts and graphically representing the area under a graph.

Definite Integral

The integral between two limits, calculated as $\text{F}(b) - \text{F}(a)$, where $\text{F}$ is the antiderivative.

Instantaneous Velocity ($v_{\text{in}}$)$$

The average velocity for an infinitely small decimal interval of time, calculated as the derivative of displacement with respect to time ($v_{\text{in}} = \frac{ds}{dt}$).

Average Acceleration ($a_{\text{avg}}$)$$

The ratio of change in velocity ($\triangle v$) in a given interval of time to the duration of that interval ($\triangle t$).

Instantaneous Speed ($v$)

The small distance ($de$) covered by a particle in a small time interval ($dt$); it is equivalent to the magnitude of instantaneous velocity.

Instantaneous Acceleration ($a_{\text{in}}$)$$

The average acceleration for an infinite decimal interval of time, calculated as $a_{\text{in}} = \frac{dv}{dt}$.