A small object moves in one dimension according to 1 (t) = t³ – 10t² + 24t, where all distances are measured in em, and time is measured in s. We are interested in the motion of the object for the time interval between to = 0.0s and tf = 6.0 s. Set your coordinates so that positive is to the right of the origin. (a) What are the initial and final positions? Find all times for which the object passes by the origin. (b) What are the maximum distances that the object reaches to the left and right of the origin? (c) What are the initial and final velocities? Find all the times for which the object is at rest.

Physics for Scientists and Engineers, Technology Update (No access codes included)
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Chapter3: Vectors
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A small object moves in one dimension according to r (t) = t³ – 10t² + 24t, where all distances are measured
in cm, and time is measured in s. We are interested in the motion of the object for the time interval between
to = 0.0 s and tf = 6.0 s. Set your coordinates so that positive is to the right of the origin.
(a) What are the initial and final positions? Find all times for which the object passes by the origin.
(b) What are the maximum distances that the object reaches to the left and right of the origin?
(c) What are the initial and final velocities? Find all the times for which the object is at rest.
(d) What is the maximum speed of the object? When and where is this speed achieved?
(e) What are the initial and final accelerations? Find all the times for which the acceleration is zero.
(f) What are the minimum and maximum accelerations of the object?
Transcribed Image Text:A small object moves in one dimension according to r (t) = t³ – 10t² + 24t, where all distances are measured in cm, and time is measured in s. We are interested in the motion of the object for the time interval between to = 0.0 s and tf = 6.0 s. Set your coordinates so that positive is to the right of the origin. (a) What are the initial and final positions? Find all times for which the object passes by the origin. (b) What are the maximum distances that the object reaches to the left and right of the origin? (c) What are the initial and final velocities? Find all the times for which the object is at rest. (d) What is the maximum speed of the object? When and where is this speed achieved? (e) What are the initial and final accelerations? Find all the times for which the acceleration is zero. (f) What are the minimum and maximum accelerations of the object?
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