A particle moves along the x-axis, its position given by x(t) = t/1+t^2, t ≥ 0 where t is measured in secondsand x in meters. (a) Find the acceleration at time t. (b) When is the particle speeding up? (c) When is the particle slowing down?

A particle moves along the x-axis, its position given by x(t) = t/1+t^2, t ≥ 0 where t is measured in secondsand x in meters. (a) Find the acceleration at time t. (b) When is the particle speeding up? (c) When is the particle slowing down?

University Physics Volume 1

18th Edition

ISBN:9781938168277

Author:William Moebs, Samuel J. Ling, Jeff Sanny

Publisher:William Moebs, Samuel J. Ling, Jeff Sanny

Chapter3: Motion Along A Straight Line

Section: Chapter Questions

Problem 11CQ: Is it possible for speed to be constant while acceleration is not zero?

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Concept explainers

Relative Velocity

It is a measurement of an object with regards to the other object which is moving or stable or stationary. For example, if we are traveling in a bus and the bus is moving at speed of 50km/hr, then our speed is according to the nearby passenger on the bus is zero. According to them, we are not moving. But if one person standing on the ground or road observes us from outside of the bus, according to him we are moving at a speed of 50km/hr and the bus is also moving at a speed of 50km/hr. Now, the motion is recognized by the observer, it depends on a frame of reference or observer. This is motion called relative motion.

Question

A particle moves along the x-axis, its position given by x(t) = t/1+t^2, t ≥ 0
where t is measured in secondsand x in meters.
(a) Find the acceleration at time t.
(b) When is the particle speeding up?
(c) When is the particle slowing down?

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