Notation Standards: In printed text, vectors are typically identified using bold typeface (e.g., for velocity). When writing by hand, where bolding is difficult, vectors should be indicated by underlining the letter (e.g., ).
Calculating Derived Vectors: Velocity is determined by the rate of change of displacement over time, expressed as . Acceleration is the rate of change of velocity, expressed as .
Sign Convention: Before solving a problem, always define a positive direction (e.g., 'upwards is positive'). Any vector acting in the opposite direction must then be assigned a negative value in calculations.
Check the Units: Always ensure that your final answer uses the correct S.I. units. Scalars like speed use , while vector acceleration uses .
Directional Context: If a question asks for a vector quantity (like velocity), your answer is incomplete without a direction. You must specify 'left', 'downwards', or use a bearing/angle.
Handwriting Clarity: Examiners look for the underline notation () to distinguish vectors from scalars. Failing to underline can lead to confusion between a vector and its magnitude in complex derivations.
Negative Scalars: A common mistake is assigning a negative sign to a scalar like distance or speed. While a vector component can be negative, the magnitude (scalar) is the absolute value and cannot be less than zero.
Confusing Speed and Velocity: Students often use these terms interchangeably. Remember that an object moving in a circle at a constant speed has a constantly changing velocity because its direction is always changing.
Weight as Mass: In everyday language, people use 'weight' to mean mass. In mechanics, weight is a force (); if gravity changes, weight changes, but mass remains constant.
