Calculus: Special Edition: Chapters 1-5 (w/ WebAssign)
6th Edition
ISBN: 9781524908102
Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE
Publisher: Kendall Hunt Publishing
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Chapter 10, Problem 43SP
To determine
To find: The velocity V, the speed
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The 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) =
=
Part 1.Given that the acceleration vector is a(t)=(−16cos(−4t))i+(−16sin(−4t))j+(3t)k the initial velocity is v(0)=i+k, and the initial position vector is r(0)=i+j+k, compute:
A. The position vector r(t)
B. The velocity vector v(t)
Part2.Find the arclength of the curve r(t)=⟨72–√t,e7t,e−7t⟩r(t)=⟨72t,e7t,e−7t⟩, 0≤t≤1
At time t = 0, a particle is located at the point (5,9,4). It travels in a straight line to the point (2,1,3), has speed 5 at (5,9,4) and constant acceleration - 3i-8j - k. Find an equation for the position
vector r(t) of the particle at time t.
The equation for the position vector r(t) of the particle at time t is r(t) =
(Type exact answers, using radicals as needed.)
i+
j+ k.
Chapter 10 Solutions
Calculus: Special Edition: Chapters 1-5 (w/ WebAssign)
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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