## 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 $t=1$

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