Unit Kinematics Module One Dimensional Motion with Constant Acceleration page 1 of 1 Describing Motion Under Constant Acceleration If acceleration is constant the equations v f v i a t and xf x i v i t 1 2 a t completely describe one dimensional motion 2 The equation v f 2 v i 2 2a x is useful if you don t have information about time intervals If acceleration is constant and you know the position and velocity of an object at an instant in time these two equations allow you to predict the motion of the object at any point in time Rearranging the definition for average acceleration and using the definition for v v f v i results in the equation v f v i a t Because we make the assumption of constant acceleration average acceleration is the same as the acceleration at any point in time a a Substitution leads to the first master equation of kinematics v f v i a t Rearranging the definition for average velocity and using the definition for x xf xi results in the equation xf xi v t When acceleration is positive and constant velocity increases lineraly 1 and v v i v f Substitution results in the 2 1 equation xf xi v i v f t Using the first 2 master equation of kinematics you can substitute v i a t for vf The result is an equation for the final position of an object in terms of its initial position initial velocity acceleration and time This is the second master equation of kinematics 1 2 x f x i v t a t 2 The final master equation of kinematics can be derived from the first two It is most useful when you don t have information about the change in time required for the motion of an object www thinkwell com info thinkwell com Copyright 2001 Thinkwell Corp All Rights Reserved 1804 doc rev 03 22 2001
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