Show work for a, b, and c

Question

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

(a)Write a formula for the average velocity of the ball for 𝑡near 1.

(b)Find the average velocity during each time period: [1,2];[1,2.001];[1,1.1];[1,1.01];[1,1.001]. Give each value rounded to 3decimals and with correct units.

(c)Estimate for the instantaneous velocity of the particle at 𝑡=1𝑠?

Answer 1

(c) derivative is 3* pi* cos(pi * t) - 2 * pi * sin(pi*t)

t=1 --> 3 * pi * cos(pi) - 2 * pi * sin(pi) =

3 * pi * (-1) - 2 * pi * 0 = - 3*pi

which is approximately -9.42478-

(a) Average Velocity = [ s(T) - s(t0) ]/ [ T - t0]

(b)