The displacement (in centimeters) of a particle s moving back and forth along a straight line is given by the equation s = 3 sin(𝜋t) + 3 cos(𝜋t), where t is measured in seconds. (Round your answers to two decimal places.)

Question

(a)Find the average velocity during each time period.
(i)[1, 1.01]cm/s
(ii)[1, 1.001]cm/s

(b)Estimate the instantaneous velocity of the particle when t = 1.

Answer 1

when t = 1, s = 3sinπ + 3 cosπ = 3(0) + 3(-1) = -3
when t = 1.01, s = 3sin(1.01π) + 3cos(1.01π) = -3.0927
when t = 1.001, s = 3sin(1.001π) + 3cos(1.001π) = -3.00949958

avg velocity between t = 1 and t = 1.01 = (-3.0927 + 3)/(1.01-1)
= appr -9.28

avg velocity between t = 1 and t = 1.001 = (-3.0094... + 3)/.001
= appr -9.41

btw, just in case you may be interested -3π = -9.425
mmmhhh?