Linear motion: Definitions, equations and units of vectors.

The idea

A vector is a quantity with both magnitude and direction, unlike a scalar which has magnitude only. In linear motion, displacement, velocity, acceleration, weight and momentum are vectors; distance, speed, mass and time are scalars. Vectors are represented by arrows: length shows magnitude, arrowhead shows direction. Equations include velocity = displacement ÷ time (v = s ÷ t), acceleration = change in velocity ÷ time (a = Δv ÷ t), weight = mass × gravitational field strength (W = m × g) and momentum = mass × velocity (p = m × v). Units: displacement in metres (m), velocity in metres per second (m s⁻¹), acceleration in metres per second squared (m s⁻²), weight in newtons (N) and momentum in kilogram metres per second (kg m s⁻¹). Always state direction with a vector answer, for example 5 m s⁻¹ north.

What earns the marks

• Defines a vector as a quantity with magnitude and direction, and a scalar as magnitude only.
• Identifies displacement, velocity, acceleration, weight and momentum as vectors in linear motion.
• States the equation velocity = displacement ÷ time with consistent units.
• States the equation acceleration = change in velocity ÷ time with consistent units.
• States the equation weight = mass × gravitational field strength and gives weight in newtons.
• States the equation momentum = mass × velocity and gives momentum in kg m s⁻¹.
• Uses correct units: m, m s⁻¹, m s⁻², N and kg m s⁻¹, with direction where required.

Common mistakes and how to put them right

• Treating speed as a vector.

  Put it right: Speed is a scalar with magnitude only, whereas velocity is a vector and needs a stated direction.

• Confusing mass and weight.

  Put it right: Mass is a scalar measured in kilograms, while weight is a vector force measured in newtons and calculated as W = m × g.

• Omitting direction from a vector answer.

  Put it right: A velocity of 5 m s⁻¹ is incomplete; write 5 m s⁻¹ north or another stated direction.

• Using the wrong unit for momentum.

  Put it right: Momentum is measured in kg m s⁻¹, not N or J.

Exam tips

• In multiple-choice questions, eliminate options that give a scalar unit for a vector quantity or omit direction.
• Check that every equation you use has matching units before substituting numbers.
• When a question asks for velocity, acceleration, weight or momentum, include both the numerical value with its unit and the direction if the quantity is a vector.