13.4 Motion in Space-Velocity and Acceleration

13.4 Motion in Space-Velocity and Acceleration - Math 224...

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Math 224 – Calculus III 1 13.4 Motion in Space: Velocity and Acceleration Recommended Homework: #1 – 37. (Omit: Kepler’s Law of Planetary Motion p. 844 to end) Velocity in Space Consider a particle that is moving along the curve ( ) ( ), ( ), ( ) t f t g t h t r . In 13.2 we saw that () t r is the tangent vector to the curve, that is, the direction of t r gives the direction of the curve at time t . More generally (and analogously to the Cartesian situation), the magnitude of t r also gives the speed of the particle at time t . Of course, in physics, velocity and acceleration are vectors, and in fact the velocity vector is t r : Velocity, ( ) ( ) tt vr and Speed = t r Acceleration ( ) ( ) av Examples: For the given position function t r , find the velocity, acceleration and speed of the particle at the indicated time: 2 ( ) ( 1) ( (2 ) t t t t r i j k when 1 t 4 ( ) (sec ) (tan ) 3 t t t t r i j k when /6 t
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Math 224 – Calculus III 2 Example: Find the position vector for the particle that has acceleration 2 ( ) (2 ) ( ) ( ) tt t t e e a i j k and where (0) vk and (0) r j+k .
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This note was uploaded on 10/31/2010 for the course MATH 224 taught by Professor Harris during the Fall '09 term at Illinois Central.

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13.4 Motion in Space-Velocity and Acceleration - Math 224...

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