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Distance and displacement review

Review key concepts, equations, and common misconceptions related to distance and displacement.

Key terms

Coordinate systemSystem we define to describe position. The origin is the point we label as zero. Coordinate systems also define directions for positive and negative numbers.
PositionLocation of an object relative to the origin. We often use the symbol x to refer to position.
DisplacementChange in position of an object. We use the symbol delta, x for displacement, where delta means "change." A vector quantity with units of start text, d, i, s, t, a, n, c, e, end text.
DistanceTotal amount the object has moved. This depends on the whole path traveled, not just the starting and ending points. Distance traveled is always a non-negative number. A scalar quantity with units of start text, d, i, s, t, a, n, c, e, end text.
Reference frameA point of view from which measurements can be made. All frames of reference are equally valid.


EquationSymbol breakdownMeaning in words
delta, x, equals, x, minus, x, start subscript, 0, end subscriptdelta, x is the displacement, x is the final position, and x, start subscript, 0, end subscript is the initial positionDisplacement is the difference between the final and initial positions

Common mistakes and misconceptions

  • People sometimes swap the initial and final positions in the displacement equation. It's easy to get mixed up and put the initial position first in the displacement equation to get minus, delta, x instead of delta, x. When calculating displacement, make sure to start with the final position and then subtract the initial position.
  • People sometimes think that distance and displacement are just different names for the same quantity. However, distance and displacement are different concepts. If an object changes direction in its journey, the total distance traveled will be greater than the displacement between those two points.
The difference between distance and displacement. Image from Wikimedia Commons, CC BY-SA 3.0
  • People sometimes get confused about choosing the “correct” coordinate system. All coordinate systems are equally valid, so we can choose any system. The choice will affect the numbers in the calculation, but as long as we use the coordinate system consistently, the physical meaning of the answer won't change.

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