An object’s position is given by x = bt + ct3 , x in meters, t in seconds, b = 1.50 m/s and c = 0.640 m/s3 . To study the limiting process leading to the instantaneous velocity, calculate the object’s average velocity over time intervals from (a) 1.00 s to 3.00 s, (b) 1.50 s to 2.50 s, and (c) 1.95 s to 2.05 s.

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter2: Motion In One Dimension

Section: Chapter Questions

Problem 48P: A commuter train travels between two downtown stations. Because the stations are only 1.00 km apart,...

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Question

An object’s position is given by x = bt + ct3 , x in meters, t in seconds, b = 1.50 m/s and c = 0.640 m/s3 . To study the limiting process leading to the instantaneous velocity, calculate the object’s average velocity over time intervals from (a) 1.00 s to 3.00 s, (b) 1.50 s to 2.50 s, and (c) 1.95 s to 2.05 s. (d) Find the instantaneous velocity as a function of time by differentiating, and compare its value at 2.00 s with your average velocities.

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