Kinematics: Vectors, Scalars, and Motion

Vocabulary flashcards covering the fundamentals of vectors, scalars, kinematic equations, and gravitational motion based on the provided lecture notes.

Vectors

Quantities that possess both magnitude and direction, such as acceleration, velocity, momentum, and force.

Scalars

Quantities that possess only magnitude, such as time, volume, speed, and mass.

Displacement

A vector quantity that describes how "out of place" an object is.

Distance

A scalar quantity that describes how far an object traveled to get out of place.

Average Speed

The total distance traveled ($s$) divided by the duration of travel ($t$).

Average Velocity

The total displacement ($s$) divided by the duration of travel ($t$).

Instantaneous Speed

The speed of an object at a certain instant in time, calculated as the derivative of the distance with respect to $t$: $\frac{ds}{dt}$.

Instantaneous Velocity

The velocity of an object at a certain instant in time, calculated as the derivative of the displacement with respect to $t$: $\frac{ds}{dt}$.

Acceleration

A vector quantity representing the changing of an object’s velocity with time, with dimensions of length per time squared and units commonly expressed as $m/s^2$.

Average Acceleration ($\bar{a}$)

The change of velocity over the change in time, defined by the formula $\bar{a} = \frac{\Delta v}{\Delta t} = \frac{v_f - v_i}{t_f - t_i}$.

Instantaneous Acceleration

The acceleration of an object at a specific point of time, written as the first derivative of velocity or the second derivative of displacement: $a = \frac{dv}{dt} = \frac{d^2s}{dt^2}$.

1D Motion with Constant Velocity Graph

A straight line on an $s$ vs $t$ graph where the final position is calculated as $s = s_0 + vt$.

1D Motion with Constant Acceleration

Motion where the $v$ vs $t$ graph is a straight line; if $a > 0$, velocity is increasing, and if $a < 0$, velocity is decreasing.

The Big Four

The basic equations of kinematics for constant acceleration: 1) $v_f = v_0 + at$, 2) $s = v_0t + \frac{1}{2}at^2$, 3) $v_f^2 = v_0^2 + 2as$, and 4) $s = \frac{v_f + v_0}{2}t$.

Free Fall

The motion of objects in a vacuum experiencing acceleration due to Earth’s gravitational pull ($g$).

Gravitational Acceleration ($g$)

The acceleration experienced by objects on Earth, roughly $9.81\text{ m/s}^2$ (or $9.80\text{ m/s}^2$ in Boston), often approximated as $10\text{ m/s}^2$ for physics tests.

Terminal Velocity

The constant velocity reached when the buoyancy force, air friction, and gravity are at equilibrium, such as the $200\text{ km/hr}$ typical for skydivers.