Week 1: Measurement and 1D Kinematics

Displacement

The difference between the current position and the starting position, which has both magnitude and direction.

Distance

The total length of the path travelled between two positions, which has magnitude only.

Average Velocity

The total displacement divided by the total time taken to travel between two points; it is a vector quantity.

Instantaneous Velocity

The limit of average velocity as the time interval approaches zero; represents the velocity at a specific moment.

Acceleration

The rate of change of velocity of an object; is a vector quantity.

Average Speed

The total distance travelled divided by the total time taken, which does not have direction.

Instantaneous Speed

The magnitude of the instantaneous velocity; represents how fast an object is moving at a specific time.

Constant Acceleration

The acceleration of an object that remains constant over time.

Deceleration

Negative acceleration, where an object slows down as acceleration and velocity are in opposite directions.

Kinematic Equations

Equations that relate position, velocity, acceleration, and time for motion with constant acceleration.

Variable Acceleration

A scenario where an object's acceleration changes over time.

Position Vector

Position includes both magnitude and direction, indicating where an object is located in relation to a reference frame or origin. It is represented as a vector that points from the origin to the object's position.

Magnitude

The size or length of a vector; a scalar value without direction.

Reference Frame

A coordinate system used to define the position and motion of an object relative to a fixed point.

Coordinate System

A method of defining the direction of movement as positive or negative, often applied in one-dimensional problems.

Two-Dimensional Coordinate System

A system that includes two axes, commonly labeled as x and y, to define a position in a plane.

Three-Dimensional Coordinate System

An extension of the 2-D system to include a third axis (z), allowing for the representation of objects in space.

Combining Reference Frames

The process of determining the overall motion of an object based on the motion of itself and any moving reference frame, as illustrated by a person on a moving train.

Estimation

The process of approximating the value of physical quantities using various techniques like making quick calculations by rounding values to one significant figure and expressing them in powers of ten.

Mean

The average value of a set of numbers, calculated by summing all values and dividing by the number of values.

Standard Deviation (σ)

A measure of the amount of variation or dispersion in a set of values.

Standard Error (∆x)

An estimate of the variability of the sample mean, calculated as the standard deviation divided by the square root of the sample size (N).

Sample Size (N)

The number of observations in a data set used to calculate statistics, affecting the precision of estimates such as the mean.

Data Deviation (di)

The difference between an individual data point and the mean of the data set. Calculated by (standard deviation) - (mean).

Best Estimate

The most accurate approximation of a population parameter based on sample data.

SI Units

Système International Units used in nearly every country, derived from 7 base units: length (m), time (s), mass (kg), temperature (K), electric current (A), amount of substance (mol), luminous intensity (cd).

Scientific Notation

A method of writing numbers using powers of ten to express significant figures clearly.

Dimensional Analysis

A technique for analyzing the units of physical quantities in an equation to ensure dimensional consistency.

Derived Quantity

A quantity that is derived from base quantities, such as speed (distance/time) and kinetic energy (1/2 mass × speed^2).

Significant Figures

The digits in a number that contribute to its precision, indicating the reliability of a measurement.

Absolute Uncertainty

The uncertainty associated with a measurement, represented as $\,\Delta x$ .It provides a range within which the true value is expected to lie.

Relative Uncertainty

A measure of the size of the absolute uncertainty relative to the actual measurement, given by $\text{relative uncertainty} = \frac{\Delta x}{x}$ and is unit-less. Usually expressed as a percentage.

Uncertainty Propagation (addition or subtraction)

When adding or subtracting quantities, the absolute uncertainty in the result is the sum of the absolute uncertainties in the values: $\Delta C = \Delta A + \Delta B$.

Uncertainty propagation (multiplication or division)

When multiplying or dividing quantities, the relative uncertainty in the result is the sum of the relative uncertainties in the values: $\frac{\Delta C}{C} = \frac{\Delta A}{A} + \frac{\Delta B}{B}$.

Accuracy

How close a measurement is to the correct value for that measurement.

Precision

Refers to how close the agreement is between repeated measurements.

Random Uncertainties

Variations that occur randomly and produce errors with equal probability of being larger or smaller than the true value.

Systematic Errors

Errors that consistently occur larger or smaller than the true value due to identifiable factors. Can be corrected.

Uncertainty

An estimate of the amount by which the measured value could vary.