Motion along a straight line: Displacement, speed, velocity, acceleration.

The idea

These four quantities describe motion along a straight line. Displacement is the vector change in position, so it has magnitude and direction; a walk of 3 m east then 4 m west gives displacement 1 m west but distance travelled 7 m. Speed is the scalar rate of change of distance, while velocity is the vector rate of change of displacement, so a car on a roundabout can have constant speed but changing velocity. Acceleration is the vector rate of change of velocity, produced by a resultant force; it can be positive or negative relative to a chosen direction. Average values use total change divided by total time, whereas instantaneous values describe a single moment. In calculations, choose a positive direction, assign signs consistently, and use v = Δs/Δt and a = Δv/Δt.

What earns the marks

• Defines displacement as a vector quantity giving the straight-line distance and direction from the starting point to the finishing point, and distinguishes it from scalar distance travelled.
• Defines speed as the scalar rate of change of distance and velocity as the vector rate of change of displacement, including direction or sign.
• Defines acceleration as the vector rate of change of velocity, recognising that a change in direction or a change in speed both produce acceleration.
• Applies v = Δs/Δt and a = Δv/Δt correctly, including consistent sign conventions and appropriate units such as m, m s⁻¹ and m s⁻².
• Distinguishes average values from instantaneous values, for example using total displacement divided by total time for average velocity.
• Interprets negative values as directions relative to a chosen positive axis rather than as automatically meaning slower or smaller.

Common mistakes and how to put them right

• Treating distance and displacement as interchangeable.

  Put it right by stating that distance is scalar and displacement is vector, then calculating each separately.

• Assuming an object moving at constant speed cannot be accelerating.

  Put it right by explaining that acceleration occurs whenever velocity changes, including a change in direction.

• Using speed and velocity as synonyms in written answers.

  Put it right by including direction or a sign whenever velocity is quoted.

• Forgetting to convert units such as km h⁻¹ to m s⁻¹ before substitution.

  Put it right by converting to SI units first.

Exam tips

• State the positive direction at the start of a calculation and keep the same sign convention throughout.
• When asked to compare scalar and vector quantities, name the quantity, give its definition and give one clear example.
• Show the equation, substitution and unit in calculation answers so that method and final value are both visible.
• Use the wording of the question to decide whether average or instantaneous values are required.