Calculus
7th Edition
ISBN: 9781524916817
Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE
Publisher: Kendall Hunt Publishing
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Chapter 10.5, Problem 6PS
To determine
To find the tangential and normal components of the object’s acceleration for the position
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At time t = 0, a particle is located at the point (8,4,7). It travels in a straight line to the point (3,9,6), has speed 3 at (8,4,7) and constant acceleration negative 5i + 5 j - k. Find an equation for the position vector r(t) of the particle at time t.
If r(t) = cos(2t)i + sin(2t)j + 3tk, compute the
tangential and normal components of the acceleration.
vector.
Tangential component at(t)
Normal component an(t)
=
=
4 Suppose the position vector of a particle in space at time t is given by: r =
(12t,-312,-8t/2)
(a) Find the particle's velocity and acceleration vectors.
(b) Find the particle's speed and direction of motion.
Chapter 10 Solutions
Calculus
Ch. 10.1 - Prob. 1PSCh. 10.1 - Prob. 2PSCh. 10.1 - Prob. 3PSCh. 10.1 - Prob. 4PSCh. 10.1 - Prob. 5PSCh. 10.1 - Prob. 6PSCh. 10.1 - Prob. 7PSCh. 10.1 - Prob. 8PSCh. 10.1 - Prob. 9PSCh. 10.1 - Prob. 10PS
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- The position of a particle in the xy-plane t time t is r(t) = (e') i+ i. Find an equation in x and y whose graph is the path of the particle. Then find the particle's velocity and acceleration vectors at t= In 7. The equation for the path of the particle is y = The velocity vector at t= In 7 is v = ( )i+( )j. (Simplify your answers.) The acceleration vector at t= In 7 is a= ()i+( )i. (Simplify your answers.)arrow_forwardThe motion of a point on the circumference of a rolling wheel of radius 4 feet is described by the vector function r(t) = 4(18t – sin(18t))i + 4(1 − cos(18t)) Find the velocity vector of the point. v(t) = Find the acceleration vector of the point. a(t) = Find the speed of the point. s(t)arrow_forwardThe motion of a point on the circumference of a rolling wheel of radius 4 feet is described by the vector function r(t) = 4(12t - sin(12t))i + 4(1 − cos(12t))j Find the velocity vector of the point. v(t) = Find the acceleration vector of the point. a(t) = Find the speed of the point. s(t) = =arrow_forward
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