Motion in a Straight Line Flashcards

Key vocabulary and concepts regarding rectilinear motion, kinematics, and uniformly accelerated motion as covered in Chapter 2.

Motion

The change in position of an object with time.

Rectilinear motion

The study of motion of objects along a straight line.

Point object

An approximation used when the size of an object is much smaller than the distance it moves in a reasonable duration of time.

Kinematics

The study of ways to describe motion without going into the causes of motion.

Instantaneous velocity

The limit of the average velocity as the time interval $\Delta t$ becomes infinitesimally small, represented by the differential coefficient $v = \frac{dx}{dt}$.

Instantaneous speed

The magnitude of the instantaneous velocity at a particular instant.

Average acceleration

The change in velocity divided by the time interval over which the change occurs, expressed as $\bar{a} = \frac{v_2 - v_1}{t_2 - t_1} = \frac{\Delta v}{\Delta t}$.

Instantaneous acceleration

The limit of the average acceleration as the time interval $\Delta t$ goes to zero, represented by $a = \frac{dv}{dt}$.

Positive acceleration graph

A position-time ($x\text{-}t$) graph that curves upward.

Negative acceleration graph

A position-time ($x\text{-}t$) graph that curves downward.

Zero acceleration graph

A position-time ($x\text{-}t$) graph that is a straight line.

Area under velocity-time graph

A graphical feature that represents the displacement of the object over a given time interval.

Uniformly accelerated motion

Motion in which the magnitude and the direction of acceleration remain constant during the course of motion.

First kinematic equation

The relationship between final velocity ($v$), initial velocity ($v_0$), acceleration ($a$), and time ($t$) given by $v = v_0 + at$.

Second kinematic equation

The relationship between displacement ($x$), initial velocity ($v_0$), time ($t$), and acceleration ($a$) given by $x = v_0t + \frac{1}{2}at^2$.

Third kinematic equation

The relationship between final velocity ($v$), initial velocity ($v_0$), acceleration ($a$), and displacement ($x$) given by $v^2 = v_0^2 + 2ax$.

Free fall

The motion of an object released near the surface of the Earth that is accelerated downward under the influence of gravity alone, neglecting air resistance.

Acceleration due to gravity ($g$)

The constant acceleration of an object in free fall near the Earth, which is approximately $9.8\,m/s^2$ (or $10\,m/s^2$ for simplified calculations).

Galileo’s law of odd numbers

The observation that distances traversed during equal intervals of time by a body falling from rest stand to one another in the same ratio as the odd numbers beginning with unity ($1:3:5:7...$).

Stopping distance

The distance a moving vehicle travels before stopping after brakes are applied, which is proportional to the square of the initial velocity ($d_s = \frac{-v_0^2}{2a}$).

Reaction time

The time elapsed between a person observing a situation, thinking, and acting.