SUVAT Sign Mistakes That Flip Your Answer

Constant-acceleration equations only work if you pick one positive direction and stick to it. These traps show where signs usually go wrong.

v = u + at · s = ut + ½at² · v² = u² + 2as — Pick one positive axis for the whole problem

Trap 1: Treating every slowdown as “a is negative” without a defined axis

Wrong: Car slows from 20 m/s to 10 m/s → student writes a = −5 without saying which way is positive.

Right: If forward is positive and the car slows while moving forward, a is negative. State the axis first.

Fix: Negative acceleration means velocity is becoming less positive — not always “going backward.”

Wrong: Walk 4 m forward and 1 m back → put s = 5 m into SUVAT.

Right: Displacement is net change: s = +3 m if forward is positive. Distance traveled is 5 m.

Fix: SUVAT uses displacement s, not total path length.

Wrong: u = +12, a = −3, s = +16 → computing as if everything were positive magnitudes only.

Right: Keep signed values: v² = (12)² + 2(−3)(16) = 144 − 96 = 48 → |v| = √48.

Fix: Square roots give ±v; the sign of v comes from the physical direction you chose.

Wrong: Taking up as positive for u but down as positive for g in the same line.

Right: If up is positive, g ≈ −9.8 m/s². If down is positive, g ≈ +9.8 m/s². One choice only.

Fix: Write “up positive” or “down positive” at the top of the working.

Wrong: Known u, v, t — but using s = ut + ½at² without finding a first (or picking the equation that omits a).

Right: Use s = ½(u + v)t when a is unknown, or find a = (v − u)/t first.

Fix: List knowns, then pick the equation that does not need the missing symbol.

Choose one positive direction, write it down, and keep every u, v, a, and s consistent with that choice.

No. It means velocity is decreasing along your positive axis. The object can still be moving forward while slowing down.

No. Displacement is net position change (signed). Distance is path length (≥ 0).