The automobile is originally at rest, i.e., s (t = 0 s) = 0 m. If it then starts to increase its speed at a (t) = (0.05t2 ) ft/s 2 , where t is in seconds, then determine the magnitudes of its velocity and acceleration at s = 550 ft. Note that a (t) becomes a t (t) along the circular path.
The automobile is originally at rest, i.e., s (t = 0 s) = 0 m. If it then starts to increase its speed at a (t) = (0.05t2 ) ft/s 2 , where t is in seconds, then determine the magnitudes of its velocity and acceleration at s = 550 ft. Note that a (t) becomes a t (t) along the circular path.
Glencoe Physics: Principles and Problems, Student Edition
1st Edition
ISBN:9780078807213
Author:Paul W. Zitzewitz
Publisher:Paul W. Zitzewitz
Chapter1: A Physics Toolkit
Section: Chapter Questions
Problem 47A
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The automobile is originally at rest, i.e., s (t = 0 s) = 0 m. If it then starts to
increase its speed at a (t) = (0.05t2 ) ft/s 2 , where t is in seconds, then determine the magnitudes of
its velocity and acceleration at s = 550 ft. Note that a (t) becomes a t (t) along the circular path.
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Step 1: Function of acceleration in terms of velocity
VIEWStep 2: Integrate and substitute to obtain the velocity function
VIEWStep 3: Function of velocity in terms of distance
VIEWStep 4: Integrate and substitute to calculated time
VIEWStep 5: Velocity of the automobile
VIEWStep 6: Centripetal acceleration and tangential acceleration
VIEWStep 7: Net acceleration at s = 550 ft
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