Question

A spring is moving up and down according to the function s(t) = -4cos(t).

Part a) Find the first derivative and calculate the velocity of the spring at t= 3pi/4?

Part b) Is the spring moving upward or downward at this point? Justify your answer.

Answer 1

The derivative of -4cos(t) is -4d/dt cos(t)=-4*-sin(t)=4sin(t).

Answer 2

Since the first function was the function of position the derivative is the function of velocity. so all you have to do now is plug 3pi/4 into the s'(t) function. That will be the velocity of the spring at that point and if its positive or not is the up or down.

Answer 3

Thanks, cleared up a small doubt I had.

Answer 4

yes i totes agree with that answer

Answer 5

Seems legit