Scalars, vectors and one-dimensional motion

What you will learn

Velocity as a vector; distance as a scalar; displacement and direction.

Specification mapping: B1.3, B1.3.1, B1.3.2

Prerequisites: B1.1, B1.2

Physical principles

A scalar has magnitude only; examples include distance, time, mass, speed and energy. A vector has magnitude and direction; examples include displacement, velocity, acceleration, force and momentum. Include direction or a defined sign when giving a vector answer.

Distance is the length of the actual path. Displacement is the straight-line change in position from start to finish. In one dimension choose a positive axis and add directed changes algebraically. Average velocity is displacement divided by elapsed time. Speed is the magnitude of instantaneous velocity, but average speed need not equal the magnitude of average velocity.

Changing direction changes velocity even when speed is constant, so motion around a bend involves acceleration. A negative velocity means motion in the negative direction; a negative displacement specifies the final position relative to the chosen origin. These signs do not imply negative distance or negative elapsed time.

Scientific diagram and interpretation

Worked examples and applications

Common misconceptions

A constant speed does not guarantee constant velocity when direction changes.

Examination technique

Name your coordinate direction and keep distance separate from signed displacement.

For an explanation, connect the physical cause to its effect. For a calculation, state the model, rearrange before substitution, retain intermediate digits, and finish with units. For a data question, refer to the actual readings and distinguish a trend from proof of a cause.

Check your understanding

Five questions. Choose an option, then Check Answer. Read the feedback and use Try Again to reset. Use Tab between controls, arrow keys within radio groups, and Enter or Space on buttons. These local practice answers are not saved.