Question

The displacement (in centimeters) of a particle moving back and forth along a straight line is given by the equation of motion s = 3sin(ðt) + 5cos(ðt), where t is measured in seconds. (Round all answers to the nearest hundredth.)
(a) Find the average velocity during the time period [1, 2].
cm/s

(b) Find the average velocity during the time period [1, 1.1].
cm/s

(c) Find the average velocity during the time period [1, 1.01].
cm/s

(d) Find the average velocity during the time period [1, 1.001].
cm/s

(e) Estimate the instantaneous velocity of the particle when t = 1.
cm/s

Answer 1

That should be sin(pi times t) not whatever symbol is up there.. sorry

Answer 2

Nevermind I figured it out

Answer 3

a) to d) are all done the same way

I will do b)

when t=1
s = 3sin(pi) + 5 cos (pi)
= -5
when t=1.1
s = 3sin(1.1pi) + 5cos(1.1pi)
= -5.682333

average velocity = (-5.682333 - (-5))/(1.1-1)
= -6.8233

Answer 4

ensure calculator is set to radians, not degrees