Not given in the exam, recall it.
What it is for
Third equation of motion is used in Force and Motion I (SPM Physics Form 4). Keep the SI units in every line of working. Force and Motion I
Symbols and SI units
| Symbol | Meaning | SI unit |
|---|---|---|
| v | final velocity | m s⁻¹ |
| u | initial velocity | m s⁻¹ |
| a | acceleration | m s⁻² |
| s | displacement | m |
Rearrangements
a = (v² − u²) / (2s)s = (v² − u²) / (2a)u = √(v² − 2as)
Worked example
Common trap
Understanding the third equation of motion
The equation v² = u² + 2as connects velocity and displacement without needing time. Here v is the final velocity in m s⁻¹, u is the initial velocity in m s⁻¹, a is the acceleration in m s⁻², and s is the displacement in m.
It is the equation to reach for whenever the question gives distance but not time. Because it links the squares of the velocities to the distance travelled, it comes directly from combining the first two equations of motion.
- To find acceleration: a = (v² − u²) / (2s)
- To find displacement: s = (v² − u²) / (2a)
- To find the initial velocity: u = √(v² − 2as)
The formula gives v², so remember to take the square root at the very end.
A worked example, step by step
A ball rolls with initial velocity u = 5 m s⁻¹ and accelerates uniformly at a = 3 m s⁻² over a displacement s = 10 m. Find the final velocity.
Write the formula, then substitute with units:
- v² = u² + 2as
- v² = (5 m s⁻¹)² + (2 × 3 m s⁻² × 10 m)
- v² = 25 m² s⁻² + 60 m² s⁻²
- v² = 85 m² s⁻²
Take the square root at the end: v = √85 = 9.22 m s⁻¹ (to three significant figures).
The unit of 2as is m s⁻² × m = m² s⁻², the same as v², confirming the working is consistent.
Common mistakes and how this is tested
The most common trap is stopping at v² and forgetting to take the square root at the end. Use this equation when time is unknown (there is no t term).
Other errors:
- Forgetting the factor 2 in the term 2as.
- Not squaring u, or writing u instead of u².
- For a deceleration, forgetting that a is negative, which can make v² smaller than u².
It appears under calculate the speed after a given distance, or determine the braking distance, and under explain why a longer stopping distance follows from a smaller deceleration. Show each squared term clearly.
Source: DSKP KSSM Physics Form 4 and 5 (Versi English), Sijil Pelajaran Malaysia: Format Pentaksiran mulai 2021, Fizik (4531) (Bahagian Pembangunan Kurikulum (BPK), KPM)