Question #a1bdc

1 Answer
Dec 8, 2015

Answer:

A displacement vector is just a way of representing a change in position. It's an arrow that points from a starting location to an ending location.

Explanation:

For example, if a person is walking on a flat surface that we have (mentally) imposed a rectangular coordinate system on, and if the person starts at the point whose rectangular coordinates are #(x,y)=(2,3)# and ends at the point whose rectangular coordinates are #(x,y)=(-4,7)#, then the displacement vector can be drawn as an arrow staring at #(2,3)# and ending at #(-4,7)#. The time elapsed is irrelevant for determining the displacement vector (but not irrelevant for determining the average velocity vector).

The so-called "components" of the displacement vector are the differences of the corresponding coordinates: #-4-2=-6# and #7-3=4# (the displacement is 6 units to the left and 4 units upward in the plane the person is walking on). The vector is then often written algebraically as #vec(v)=-6hat(i)+4hat(j)#, where #hat(i)# is a "unit" vector (length one) pointing directly to the right (in the positive #x#-direction) and #hat(j)# is a unit vector pointing directly upward (in the positive #y#-direction) in the plane the person is walking on.

The person does not have to walk in a straight line, but the displacement vector itself is straight.