Scalars, Vectors, and What a Minus Sign Means

Saying a car moves at 30 m/s tells you nothing about where it ends up, because speed alone has no direction attached. Pick a direction, call it positive, and the opposite direction becomes negative. That single choice turns speed into velocity, and distance into displacement. Displacement only cares about where you started and where you ended up, not the path in between or how far you actually traveled getting there.

The minus sign is a direction label, not a speed judgment. A velocity of -20 m/s means motion in the negative direction, full stop. Whether the object is speeding up or slowing down depends on what the velocity is doing over time, not on its sign alone. If velocity goes from -12 m/s to -20 m/s, the object is moving further from zero while staying negative, so it is speeding up in the negative direction. Speed is the size of velocity, the number with the sign stripped off, so a more negative velocity still means a larger speed.

This distinction sets up everything else in kinematics. Position-time, velocity-time, and acceleration-time graphs all depend on sign conventions to show direction, and reading them wrong because you treat negative as automatically slower is the single easiest way to misread a graph. Once you're comfortable separating magnitude from direction here, acceleration works the same way: its sign tells you which way it points, and only comparing it to the velocity's sign tells you whether the object speeds up or slows down.