Unit Kinematics Module Describing Motion in Two and Three Dimensions page 1 of 2 Relating Position Velocity and Acceleration Vectors in Two Dimensions dv dr The vector equations a and v contain information about motion in the dt dt x and y directions Drawing pictures with vectors is a useful way to visualize two dimensional motion Take the derivative of the components of the position vector to find the velocity vector take the derivative of the components of the velocity vector to find the acceleration vector Motion in two dimensions is richer than motion in one dimension The vector equations for acceleration and velocity contain information about motion in both the x and y directions The position of an object as a function of time is m m given by the equation r 5 t i 5 2 t 2 j s s You can find the equation for object s velocity vector as a function of time by taking the time derivative of dr m m 5 i 10 2 t j its position function v dt s s Similarly you can find the equation for the object s acceleration vector as a function of time by taking the time derivative of its velocity function dv m a 10 2 j dt s www thinkwell com info thinkwell com Copyright 2001 Thinkwell Corp All Rights Reserved 1814 doc rev 03 28 2001 Unit Kinematics Module Describing Motion in Two and Three Dimensions page 2 of 2 Relating Position Velocity and Acceleration Vectors in Two Dimensions The object s path is a parabola The horizontal component of the velocity is constant in time m v x 5 The vertical component of velocity s m increases 10 m each second v y 10t 2 The s object s velocity vector is always tangent to its position function Recall that the horizontal component of the object s velocity is constant As a result its acceleration has no horizontal The vertical component of the velocity increases with time so there is a vertical component of the acceleration The vertical component of the m acceleration is constant in time ay 10 2 s www thinkwell com info thinkwell com Copyright 2001 Thinkwell Corp All Rights Reserved 1814 doc rev 03 28 2001
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