Use the equation: (final velocity)² ((metre/second)², (m/s)²) – (initial…

The idea

This equation links four quantities for motion along a straight line with uniform acceleration: final velocity v, initial velocity u, acceleration a and distance (displacement) x. The squared velocities carry units of (m/s)², acceleration carries m/s² and distance carries m, so the right-hand side gives m/s² × m = m²/s², matching the left-hand side. To use it, list v, u, a and x, convert all speeds to m/s and distances to m, then substitute. Example: a car speeds up from u = 5 m/s to v = 25 m/s over x = 120 m. Then v² − u² = 625 − 25 = 600 (m/s)², so a = 600 ÷ (2 × 120) = 600 ÷ 240 = 2.5 m/s². Rearranged forms let you find v, u or x. The equation applies only when acceleration is constant and motion is in one direction.

What earns the marks

• Selects the equation v² − u² = 2 × a × x and identifies the unknown quantity before substituting.
• Converts velocities to m/s and distance to m before squaring or multiplying.
• Squares the velocities correctly, keeping the unit (m/s)² on each squared term.
• Rearranges the equation correctly, for example a = (v² − u²) ÷ (2 × x) or x = (v² − u²) ÷ (2 × a).
• States the final answer with the correct unit, such as m/s² for acceleration or m for distance.
• Recognises that the equation requires uniform acceleration along a straight line.

Common mistakes and how to put them right

• Squares only the number and drops the unit.

  Put it right: Keep (m/s)² on each squared velocity term.

• Subtracts u from v before squaring.

  Put it right: Square each velocity first, then subtract.

• Forgets the factor of 2 on the acceleration × distance side.

  Put it right: Include 2 × a × x.

• Uses the equation when acceleration changes.

  Put it right: Apply it only to uniform acceleration in one direction.

Exam tips

• Write down v, u, a and x with units before choosing the rearrangement, so the unknown is clear.
• Check the units of both sides: (m/s)² must equal m/s² × m, which is m²/s².
• Estimate the answer first, then check the calculated value is sensible for the situation described.