Problem 6 Suppose the position function of a particle moving in one dimension is given by a(t) = 5+ 3t + 212 – 0.5t (1.30) where the coefficients are such that the result will be in meters if you enter the time in seconds. What is the particle's velocity at t = 2s? There are two ways you can do this: • If you know calculus, calculate the derivative of (1.30) and evaluate it at t= 2 s. • If you do not yet know how to take derivatives, calculate the limit in the definition (1.8). That is to say, calculate Ar/At with t; = 2s and At equal, first, to 0.1s, then to 0.01 s, and then to 0.001 s. You will need to keep more than the usual 4 decimals in the intermediate calculations if you want an accurate result, but you should still report only 3 significant digits in the final result.

Problem 6 Suppose the position function of a particle moving in one dimension is given by a(t) = 5+ 3t + 212 – 0.5t (1.30) where the coefficients are such that the result will be in meters if you enter the time in seconds. What is the particle's velocity at t = 2s? There are two ways you can do this: • If you know calculus, calculate the derivative of (1.30) and evaluate it at t= 2 s. • If you do not yet know how to take derivatives, calculate the limit in the definition (1.8). That is to say, calculate Ar/At with t; = 2s and At equal, first, to 0.1s, then to 0.01 s, and then to 0.001 s. You will need to keep more than the usual 4 decimals in the intermediate calculations if you want an accurate result, but you should still report only 3 significant digits in the final result.

Name: Problem 6Suppose the position function of a particle moving in one di
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Description: Problem 6Suppose the position function of a particle moving in one dimension is given bya(t) = 5+ 3t + 2t2 – 0.5t3(1.30)where the coefficients are such that the result will be in meters if you enter the time in seconds.What is the particle's velocit

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Displacement, Velocity and Acceleration

In classical mechanics, kinematics deals with the motion of a particle. It deals only with the position, velocity, acceleration, and displacement of a particle. It has no concern about the source of motion.

Linear Displacement

The term "displacement" refers to when something shifts away from its original "location," and "linear" refers to a straight line. As a result, “Linear Displacement” can be described as the movement of an object in a straight line along a single axis, for example, from side to side or up and down. Non-contact sensors such as LVDTs and other linear location sensors can calculate linear displacement. Non-contact sensors such as LVDTs and other linear location sensors can calculate linear displacement. Linear displacement is usually measured in millimeters or inches and may be positive or negative.

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Problem 6
Suppose the position function of a particle moving in one dimension is given by
a(t) = 5+ 3t + 2t2 – 0.5t3
(1.30)
where the coefficients are such that the result will be in meters if you enter the time in seconds.
What is the particle's velocity at t= 2 s? There are two ways you can do this:
• If you know calculus, calculate the derivative of (1.30) and evaluate it at t= 2 s.
If you do not yet know how to take derivatives, calculate the limit in the definition (1.8).
That is to say, calculate Ar/At with t; = 2s and At equal, first, to 0.1s, then to 0.01 s, and
then to 0.001 s. You will need to keep more than the usual 4 decimals in the intermediate
calculations if you want an accurate result, but you should still report only 3 significant digits
in the final result.

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