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(4 points) Suppose the position (in feet) of an object moving horizontally at time t (in seconds) is s(t) = 2t3- 21t2 + 60t for 00 corresponding to positions to the right of %3D s = 0. a). Find the velocity function on the interval 0

(4 points) Suppose the position (in feet) of an object moving horizontally at time t (in seconds) is s(t) = 2t3- 21t2 + 60t for 00 corresponding to positions to the right of %3D s = 0. a). Find the velocity function on the interval 0

College Algebra
College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter3: Polynomial Functions
Section3.5: Mathematical Modeling And Variation
Problem 7ECP: The kinetic energy E of an object varies jointly with the object’s mass m and the square of the...
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(4 points) Suppose the position (in feet) of an object moving horizontally at time t (in seconds) is s(t) = 2t3- 21t2 + 60t for 0<t<7, with s>0 corresponding to positions to the right of s = 0. a). Find the velocity function on the interval 0 <t<7, and determine when the object is stationary, moving to the left, and moving to the right. b). Find the position(s) of the object when its velocity is zero, mark the position(s) on the graph. Try to explain the position(s) related to part (a). c). Find the acceleration function on the interval 0 <t < 7. On what intervals is the speed increasing? s(t), the velocity function v(t) = s'(t), and the accelera- d). Graph the position function s = tion function a(t) = v'(t) s"(t). (Graph all of them on one xy-coordinate plane.) %3D s(t) on a horizontal line (y 0,0<IS 77), indicating all interesting e). Optional: Draw r = points (t, s(t)) mentioned in (a)- (c).
Transcribed Image Text:(4 points) Suppose the position (in feet) of an object moving horizontally at time t (in seconds) is s(t) = 2t3- 21t2 + 60t for 0<t<7, with s>0 corresponding to positions to the right of s = 0. a). Find the velocity function on the interval 0 <t<7, and determine when the object is stationary, moving to the left, and moving to the right. b). Find the position(s) of the object when its velocity is zero, mark the position(s) on the graph. Try to explain the position(s) related to part (a). c). Find the acceleration function on the interval 0 <t < 7. On what intervals is the speed increasing? s(t), the velocity function v(t) = s'(t), and the accelera- d). Graph the position function s = tion function a(t) = v'(t) s"(t). (Graph all of them on one xy-coordinate plane.) %3D s(t) on a horizontal line (y 0,0<IS 77), indicating all interesting e). Optional: Draw r = points (t, s(t)) mentioned in (a)- (c).
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