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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 $s=2 \sin \pi t+3 \cos \pi t,$ wher...

Question

The displacement (in centimeters) of a particle moving back and forth along a straight line is given by the equation of motion $s=2 \sin \pi t+3 \cos \pi t,$ where $t$ is measured in seconds. (a) Find the average velocity during each time period: $$\begin{array}{ll}{\text { (i) }[1,2]} & {\text { (ii) }[1,1.1]} \\ {\text { (iii) }[1,1.01]} & {\text { (iv) }[1,1.001]}\end{array}$$ (b) Estimate the instantaneous velocity of the particle when $t=1$

The displacement (in centimeters) of a particle moving back and forth along a straight line is given by the equation of motion $s=2 \sin \pi t+3 \cos \pi t,$ where $t$ is measured in seconds. (a) Find the average velocity during each time period: $$\begin{array}{ll}{\text { (i) }[1,2]} & {\text { (ii) }[1,1.1]} \\ {\text { (iii) }[1,1.01]} & {\text { (iv) }[1,1.001]}\end{array}$$ (b) Estimate the instantaneous velocity of the particle when $t=1$



Answers

The displacement (in centimeters) of a particle moving back and forth along a straight line is given by the equation of motion $ s = 2 \sin \pi t + 3 \cos \pi t $, where $ t $ is measured in seconds.

(a) Find the average velocity during 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 $.


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