Linear motion: Definitions, equations and units of scalars.

The idea

A scalar is a quantity defined completely by magnitude alone, with no direction needed. In linear motion, key scalars include mass, inertia, distance and speed. Mass (kg) is the quantity of matter in a body. Inertia is a body's resistance to a change in motion, directly related to its mass. Distance (m) is the total path length covered. Speed (m s⁻¹) is the rate of change of distance, calculated using the equation: speed = distance ÷ time. Units must be consistent: convert grams to kilograms by dividing by 1000, and minutes to seconds by multiplying by 60. For example, 250 g = 0.25 kg and 3 minutes = 180 s. Always state the unit with the numerical answer, and check that the equation you choose matches the quantity you are asked to find.

What earns the marks

• A scalar is fully described by magnitude alone and requires no direction.
• Mass is a scalar measured in kilograms (kg), representing the quantity of matter.
• Inertia is a scalar representing a body's resistance to a change in its state of motion.
• Distance is a scalar measured in metres (m), representing the total path length.
• Speed is a scalar measured in metres per second (m s⁻¹), calculated as distance ÷ time.
• Unit conversions: 1 kg = 1000 g, so divide grams by 1000; 1 minute = 60 s, so multiply minutes by 60.

Common mistakes and how to put them right

• Treating speed as a vector.

  Put it right: Speed has magnitude only, whereas velocity includes direction, so a car travelling at 20 m s⁻¹ has that speed regardless of its heading.

• Confusing mass with weight.

  Put it right: Mass is a scalar in kg, while weight is a force in newtons (N) equal to mass × gravitational field strength.

• Using inconsistent units, such as dividing metres by minutes.

  Put it right: Convert time to seconds first so the answer is in m s⁻¹.

• Omitting the unit from the final answer.

  Put it right: A numerical value without its unit is incomplete in linear motion calculations.

Exam tips

• Underline the quantity the question asks you to find, then select the matching equation before substituting numbers.
• Convert all values to kg, m and s before calculating, then write the unit after your answer.
• Check whether the option is a scalar or a vector by asking whether a direction is needed to define it fully.