Unit Kinematics Module Describing Motion in Two and Three Dimensions page 1 of 1 The Position and Velocity Vectors For motion in two dimensions all the fundamental quantities of kinematics position displacement velocity and acceleration are vectors A good way to think about the motion of an object in two dimensions is in terms of its x and y components By considering components for example the vector forms of the equations of two dimensional or three dimensional motion can be expressed as equations of motion in one dimension We have derived equations of kinematics that describe the motion of objects in one dimension However many objects move in two or three dimensions For example the path of a ball tossed in the air follows a two dimensional arc A ship navigating a river can move forward or backward and left or right All of the fundamental quantities of kinematics that we have explored in one dimension can be written as vectors in two and three dimensions These quantities include position displacement velocity and acceleration x In t two dimensions the average velocity vector is r v The initial position of the lizard is ri and it t moves to position rf Notice that the average velocity vector v is in the same direction as r but its magnitude is different In one dimension average velocity is v r t The graph shows the path that the lizard follows as it moves in two dimensions The instantaneous velocity vector is found by taking the limit as t approaches zero of the average velocity vector r d r v lim The direction of the t 0 t dt instantaneous velocity vector is always tangent to the position function When two vectors are equivalent their components are equal in magnitude You can write the equations of kinematics as vector equations and then break them into component form www thinkwell com info thinkwell com Copyright 2001 Thinkwell Corp All Rights Reserved 1810 rev 06 25 2001
View Full Document
Unlocking...