Chapter 1: Motion in a Straight Line

Vocabulary flashcards covering measurement standards, systems of units, error types, kinematics definitions, and gravitational acceleration from Chapter 1 (Motion in a Straight Line).

Unit

An agreed reference amount of a physical quantity.

Standard

The physical realisation that fixes the size of a unit.

Primary standard

A standard that is defined by a property of nature.

Secondary standard

A standard derived from a primary standard (for example, the minute derived from the second).

Metre

The standard of length, defined today through the speed of light in vacuum, which superseded Kane's krypton-86 standard in 1983.

British system

A system of measurement that takes force (the pound) rather than mass as its base quantity.

Random error

Scatter of repeated results about their average, arising from causes such as the observer's inability to time identically each time; it is reduced by averaging many measurements.

Systematic error

A bias that shifts every result in the same direction (such as a slow watch or observer reaction time); it cannot be removed by averaging and is reduced by better instruments or improved experimental design.

Significant figures

The meaningful digits in a numerical value indicating precision, where the last digit is uncertain. In this text, numbers are treated as known to three significant figures.

Displacement ($\Delta x$)

The change in position of an object along a coordinate axis, given by $\Delta x = x_2 - x_1$.

Average velocity ($\bar{v}$)

The displacement divided by the elapsed time: $\bar{v} = \frac{\Delta x}{\Delta t} = \frac{x_2 - x_1}{t_2 - t_1}$.

Instantaneous velocity ($v$)

The average velocity evaluated over an arbitrarily short time interval, defined mathematically as $v = \lim_{\Delta t \to 0} \frac{\Delta x}{\Delta t} = \frac{dx}{dt}$.

Differentiation

The mathematical process of evaluating the limit of $\frac{\Delta x}{\Delta t}$ as $\Delta t \to 0$ to find the derivative of position with respect to time ($\frac{dx}{dt}$).

Speed

The magnitude of instantaneous velocity, which is always positive or zero.

Average acceleration ($\bar{a}$)

The change in velocity divided by the elapsed time: $\bar{a} = \frac{\Delta v}{\Delta t}$.

Instantaneous acceleration ($a$)

The derivative of velocity with respect to time ($a = \frac{dv}{dt}$), corresponding graphically to the slope of the $v\text{-}t$ graph.

Galileo's first statement on falling objects

In the absence of air resistance, gravitational acceleration is the same for all falling objects, regardless of their size or composition.

Galileo's second statement on falling objects

In the absence of air resistance, gravitational acceleration is constant and does not change as an object falls.

Acceleration of gravity ($g$)

The acceleration experienced by falling objects due to gravity in the absence of air resistance, equal to approximately $9.8\,\text{m s}^{-2}$ ($32\,\text{ft/s}^2$, or $980\,\text{cm s}^{-2}$).

Terminal velocity

The maximum, constant velocity reached by a falling object when the upward force of air resistance balances the downward pull of gravity.