(Solved): A graphing calculator is recommended. The displacement (in centimeters) of a particle s moving back ...

A graphing calculator is recommended. The displacement (in centimeters) of a particle s moving back and forth along a straight line is given by the equation \( s=5 \sin (\pi t)+2 \cos (\pi t) \), where \( t \) is measured in seconds. (Round your answers to two decimal places.) (a) Find the average velocity during each time period. (i) \( [1,2] \) \( \mathrm{cm} / \mathrm{s} \) (ii) \( [1,1,1] \) \( \mathrm{cm} / \mathrm{s} \) (iii) \( [1,1.01] \) \( \mathrm{cm} / \mathrm{s} \) (iv) \( [1,1.001] \) \( \mathrm{cm} / \mathrm{s} \) (b) Estimate the instantaneous velocity of the particle when \( t=1 \). \( \mathrm{cm} / \mathrm{s} \)