Motion quantities, SI units and conversions

What you will learn

Symbols u, v, s, t and a; metres, seconds, speed and acceleration; km s⁻¹ and km h⁻¹.

Specification mapping: B1.1, B1.1.1, B1.1.2

Prerequisites: A1.4

Physical principles

Use u for initial velocity, v for final velocity, s for displacement in a one-dimensional motion equation, t for elapsed time and a for acceleration. SI units are m, s, m s⁻¹ and m s⁻². The same symbol s can denote distance in a speed calculation; state which quantity is intended rather than relying on the symbol alone.

A kilometre is 1000 m and an hour is 3600 s. Convert km h⁻¹ to m s⁻¹ by dividing by 3.6; convert back by multiplying by 3.6. Convert km s⁻¹ to m s⁻¹ by multiplying by 1000. Keep the time denominator: km s⁻¹ is not km h⁻¹.

Acceleration measures velocity change per second. An acceleration of 2 m s⁻² means velocity changes by 2 m s⁻¹ in each second while that acceleration is maintained. A negative value describes acceleration opposite to the chosen positive direction; it does not always mean decreasing speed.

Scientific diagram and interpretation

Worked examples and applications

Common misconceptions

m s⁻² is a change in velocity per second, not a speed squared.

Examination technique

Make the positive direction explicit before assigning signs to velocities.

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.