Average Velocity & Instantaneous Velocity...4

[nycmathguy]

Chapter 1
Calculus 1

 

[MathLover1]

a.
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

average velocity between t = 1 and t = 1.01 is = (-3.0927-(-3))/(1.01-1)= -9.28cm/s ( approximately)

b.

s'=v(t)= 3 π (cos(π t) - sin(π t))
t=1
v(1)= 3 π (cos(π ) - sin(π ))
v(1)= -9.425 cm/s

 

[nycmathguy]

a.
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

average velocity between t = 1 and t = 1.01 is = (-3.0927-(-3))/(1.01-1)= -9.28cm/s ( approximately)

b.

View attachment 2348

s'=v(t)= 3 π (cos(π t) - sin(π t))
t=1
v(1)= 3 π (cos(π ) - sin(π ))
v(1)= -9.425 cm/s

Well, at least I tried. I'm not ready for the derivative of trigonometric functions. I think finding s prime involves the chain rule, which is several chapters ahead in the textbook.