Motion of an Object

     The graph of the position vector is called the trajectory of the moving object. The velocity  vector is a tangent vector to the trajectory at any point where exists and . When the object is stationary. The direction of motion and speed of an object satisfies:

Definition (Motion of an Object in Space) If an object moves in such a way that its position at time is given by the vector function then

    (i)  Velocity vector:  
    
    (ii)  Speed  
    
    (iii)  Direction of motion vector:  
    
    (iv)  Acceleration vector:  
    

Example (Motion of an Object in Space) Suppose the position vector for a particle in space at time is given by Find the particle's velocity vector, acceleration vector, speed, and direction of motion vector at time

    Solution. At time , the particle's velocity vector is



the acceleration vector is,



the speed is



and the direction of motion vector is

.



Example (Motion of an Object in Space) Find the position vector and velocity vector given the acceleration vector function initial position vector   and initial velocity vector  

    Solution.  Given the velocity vector function is
     




where and are constants to be determined. By using



Thus Therefore,



So the position vector function is



which is



where and are constants to be determined. By using



Thus Therefore,

Advanced Calculus Books

Advanced Calculus of Several Variables (Dover Books on Advanced Mathematics) List Price: $20.95 Buy New: $12.88 You Save: $8.07 (39%) New (21) Used (12) from $6.99Modern conceptual treatment of multivariable calculus, emphasizing the interplay of geometry and analysis via linear algebra and the approximation of nonlinear mappings by linear ones. At the same time, (more)

Schaum's Outline of Advanced Calculus, Second Edition List Price: $18.95 Buy New: $11.07 You Save: $7.88 (42%) New (27) Used (18) from $7.77This best-selling guide--which has sold more than 340,000 copies since its first publication--has been thoroughly updated throughout to correspons to current advanced calculus courses. A complete and comprehensive (more)

Advanced Calculus Demystified List Price: $19.95 Buy New: $11.69 You Save: $8.26 (41%) New (30) Used (12) from $8.14Your INTEGRAL tool for mastering ADVANCED CALCULUS Interested in going further in calculus but don't where to begin? No problem! With Advanced Calculus Demystified, there's no limit to how much you will (more)

Advanced Calculus for Applications (2nd Edition) List Price: $73.33 Buy Used: $18.79 You Save: $54.54 (74%) New (13) Used (27) from $18.79Advanced Calculus for Applications (2nd Edition) (more)

Advanced Calculus (5th Edition) List Price: $73.33 Buy New: $41.49 You Save: $31.84 (43%) New (21) Used (21) Collectible (1) from $22.50The Fifth Edition of this leading text offers substantial training in vectors and matrices, vector analysis, and partial differential equations. Vectors are introduced at the outset and serve at many points (more)

Advanced Calculus List Price: $18.95 Buy New: $5.75 You Save: $13.20 (70%) New (28) Used (25) from $5.49Classic text leads from elementary calculus into more theoretic problems. Precise approach with definitions, theorems, proofs, examples and exercises. Topics include partial differentiation, vectors, differential (more)

Advanced Calculus: An Introduction to Classical Analysis List Price: $29.95 Buy New: $18.38 You Save: $11.57 (39%) New (13) Used (7) from $16.18A course in analysis dealing essentially with functions of a real variable, this text for upper-level undergraduate students introduces the basic concepts in their simplest setting and proceeds with numerous (more)

• print this page
• pages linking here
• related pages