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The displacement (in centimeters) of a particle moving back and forth along a straight line is given by the equation of motion s(t) = 2 sin(at) + 3cos (at), wheret is measured in seconds. a. Find the average velocity for each time period: i. [1,2] ii. [1,1.1] iii. [1,1.01] iv. [1,1.001] b. Estimate the instantaneous velocity of the particle when t=1. Hint: Find the slope of the tangent line.

The displacement (in centimeters) of a particle moving back and forth along a straight line is given by the equation of motion s(t) = 2 sin(at) + 3cos (at), wheret is measured in seconds. a. Find the average velocity for each time period: i. [1,2] ii. [1,1.1] iii. [1,1.01] iv. [1,1.001] b. Estimate the instantaneous velocity of the particle when t=1. Hint: Find the slope of the tangent line.

College Physics
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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**Problem 3: Particle Motion and Velocity Analysis** The displacement (in centimeters) of a particle moving back and forth along a straight line is given by the equation of motion \( s(t) = 2 \sin(\pi t) + 3 \cos(\pi t) \), where \( t \) is measured in seconds. a. *Find the average velocity for each time period:* i. \([1,2]\) ii. \([1,1.1]\) iii. \([1,1.01]\) iv. \([1,1.001]\) b. *Estimate the instantaneous velocity of the particle when \( t = 1 \). Hint: Find the slope of the tangent line.*
Transcribed Image Text:**Problem 3: Particle Motion and Velocity Analysis** The displacement (in centimeters) of a particle moving back and forth along a straight line is given by the equation of motion \( s(t) = 2 \sin(\pi t) + 3 \cos(\pi t) \), where \( t \) is measured in seconds. a. *Find the average velocity for each time period:* i. \([1,2]\) ii. \([1,1.1]\) iii. \([1,1.01]\) iv. \([1,1.001]\) b. *Estimate the instantaneous velocity of the particle when \( t = 1 \). Hint: Find the slope of the tangent line.*
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