Scalars and Vectors in One and Two Dimensions
▶︎ Watch it animatedinteractive step-through · ~3 min · optionalDirection is the first thing physics asks you to track. A scalar is a single number — mass, time, kinetic energy. A vector carries size and direction. In one dimension that direction is just a sign: pick which way is positive and stay consistent. In two dimensions it lives in the unit vectors î and ĵ, and any vector is a sum of those two, each scaled by its component. What Physics C adds is fluency — moving between the sign-convention world and the unit-vector world, and translating the moment a problem switches from one notation to the other.
The math is the easy part. What actually trips people up is the meaning of the signs: does the negative on an î-coefficient mark the −î direction (it does), or just make a smaller number (it doesn't)? And does the magnitude of a two-dimensional vector come from Pythagoras on its components (correct), or from adding the components with their signs (the trap)? Once those moves are reflexive, Physics C kinematics is mostly bookkeeping.
The work
3 ways in · any order
Lesson
Scalars and Vectors
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Scalars carry size; vectors carry size and direction. The lesson covers one-dimensional sign conventions and two-dimensional unit-vector notation, with a Physics 1 → Physics C translation table that bridges the two, and closes with a ten-scenario applet spanning category recognition, magnitudes, and component arithmetic.
Diagnostic
10-item topic check
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Ten items spanning the six in-scope misconceptions for Topic 1.1: scalar/vector category recognition, the two natures of a negative sign (sign-as-magnitude vs sign-as-state), signed-sum-as-magnitude in two dimensions, head-to-tail stacking, and component-vs-vector conflation in unit-vector form. Take it cold to surface what's still tangled, or after the lesson to confirm it isn't.
Targeted Practice
Drill a single misconception
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Pick one of the failure modes you missed and drill it on its own. The round is adaptive: two correct in a row clears the misconception and moves you to the next.