Sign convention errors are the #1 source of incorrect answers in kinematics. Here is a systematic approach:

Step 1: Choose positive direction BEFORE writing equations. Standard: rightward/upward = positive.

Step 2: Assign signs consistently:

• Upward throw: u = +$v_0$, a = -g
• Downward throw: u = -$v_0$, a = -g (if upward is positive)
• Free fall from rest: u = 0, a = -g

Step 3: Displacement sign indicates direction:

• Positive s: object is above/right of starting point
• Negative s: object is below/left of starting point

Common Errors to Avoid:

1. Using s = +h when the object is BELOW the launch point (should be -h)
2. Forgetting that g is always positive; the SIGN comes from the direction
3. Confusing distance (always positive) with displacement (can be negative)
4. Assuming acceleration = 0 when velocity = 0 (e.g., at the top of a throw)
5. Using kinematic equations when acceleration is NOT constant
6. In nth second formula: $s_n$ can be negative (body has reversed)
7. Using speed instead of velocity in vector equations

Golden Rule: When in doubt, draw a diagram with axes marked, and explicitly write the sign of every quantity.