Rectilinear Motion

    Speed is the absolute value (the magnitude) of an object's velocity. The velocity indicates both speed and direction (relative to a given coordinate system).  

Definition (Rectilinear Motion) An object that moves along a straight line with position has velocity and acceleration when these derivatives exist. The speed of an object at time is

Example (Rectilinear Motion) A particle moving along the -axis has position



after an elapsed time of seconds.

(a) Find the velocity of the particle at time

    Solution. The velocity is given by



(b) Find the acceleration at time

    Solution. The acceleration is given by
    


(c) What is the total distance travelled by the particle during the first 3 seconds?

    Solution. Since when



but is not on the distance covered is

.

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Rectilinear Motion
Published by Library of Math -- Online math organized by subject into topics.
Written by Smith, David A.
http://www.libraryofmath.com/rectilinear-motion.html