Displacement (vector) is straight-line change in position with direction; distance (scalar) is total path length traveled.
Velocity (vector, Δx/Δt) includes direction; speed (scalar, distance/Δt) does not.
Acceleration (vector, a = Δv/Δt) measures the rate of change of velocity — a change in direction alone counts as acceleration, even at constant speed.
Displacement vs. Distance
Displacement
Distance
Vector quantity
Scalar quantity
Straight-line change in position, with direction
Total path length traveled
Walk 10 m east then 10 m west: 0 m
Walk 10 m east then 10 m west: 20 m
Velocity vs. Speed
Velocity
Speed
Vector; = Δx / Δt
Scalar; = Distance / Δt
How fast, and in which direction
How fast only
Acceleration
a = Δv / Δt
a = Acceleration (m/s²)
Δv = Change in velocity
Δt = Time interval over which the change occurs
Common MCAT Trap
A car rounding a corner at constant speed is still accelerating — its direction (and therefore velocity) is changing, even though its speed isn't.
Don't average speed the same way you'd average velocity when direction reverses — round-trip velocity can be zero even when speed the whole time was nonzero.
Quick Recall
Why can displacement be zero while distance is nonzero?
Can an object accelerate without changing speed?
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