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handout 13-5

# handout 13-5 - Math 200 Spring 2010 Handout 9 Section 13-5...

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Math 200, Spring 2010 Handout 9 Section 13-5 Motion in Three Space Velocity, Speed and Acceleration Suppose a particle moves through space so that its position vector is ( ) t r at time t and ( ) t h + r at time t h + . The vector ( ) ( ) t h t h + r r gives the average velocity over a time interval h and its limit is the velocity vector ( ) t v at time t : ( ) ( ) ( ) ( ) 0 lim h t h t t t h + = = r r v r . Note that the velocity vector ( ) t v is the tangent vector ( ) t r . The speed of the particle at time t is the magnitude of the velocity vector: ( ) ( ) ( ) v t t t = = = v r rate of change of distance with respect to time. The acceleration of the particle at time t is the derivative of the velocity vector: ( ) ( ) ( ) t t t ′′ = = = a v r rate of change of the velocity with respect to time. 1. Find the velocity, acceleration, and speed of a particle with position vector ( ) 2cos sin t t t t = + + r i j k . Sketch the path of the particle and draw the velocity and acceleration vectors at the point when 0 t = .

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handout 13-5 - Math 200 Spring 2010 Handout 9 Section 13-5...

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