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displacement vs. distance traveled If a body with position function s (t) moves along a coordinate line without changing direction, we can calculate the total distance it travels from t = a to t = b.
To determine the displacement of an object, you only have to consider the change in position between the starting point and the ending point. The path followed from one point to the other does not matter.
2.6 Displacement vs. Distance. Tools: Definite and Indefinite integrals. The Calculus of Motion (2.3/2.9) (One) Limit of Applicability. v(t) = dx(t)/dt only defined for continuous functions. Math solution: Don’t use formula at discontinuities. Near frames 8/12 function not continuous. Physics solution:
Possible discussion points: By integrating the acceleration equation, you can find the velocity equation and by integrating the velocity equation, you can find the displacement equation. Also, by find the area between the curve and the x-axis, you can find displacement and total distance.
Distance: the total length between two points traveled. Vector: a physical quantity that is specified by a size and direction. Ex. Displacement: a vector that refers to "how far out of place an object is"; how far an object is from its starting position. Distance vs. Displacement Ex. Walk 1 mile to the movies and continue to walk
Displacement: The straight-line distance between the initial and final points. The symbol is Δx, where Δ means “change in” and x means “position”. The change in position of an object. Δx = xf – xi (read, displacement equals position final minus position initial) Can be either positive or negative.
This document contains examples of calculating distance and displacement from descriptions of object movement. Distance is the total path length traveled, while displacement is the straight-line distance from the starting point.
