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

Answer 1

t=3pi/4

Answer 2

I think I got it right but Im not too sure

Answer 3

Go on and post it :)

Answer 4

What do you get for the first derivative, and then evaluating it at t = 3pi/4?

Answer 5

i found the prime which was 4sin(t) i think and i just plugged in 3pi/4. Is that right?

Answer 6

then that just gives me 2.828

Answer 7

Yes, that is correct.

Answer 8

The derivative of cos(x) is -sin(x). So -4 * -sin(x) gives 4sin(x). It is right.

Answer 9

and for part b?

Answer 10

umm well im assuming because i got positive its going upwards :/

Answer 11

but that's just an assumption. i think im pretty sure i have to graph it out and see how the graph is moving

Answer 12

wait, looks like the graph is going downwards so i guess the spring is also downwards right?

Answer 13

the 1st derivative is the instantaneous slope at that point, so if it is positive, the function is increasing. The value of the function is the position, so I think you have made a reasonable interpretation.

Answer 14

oh ok then i guess that's correct

Answer 15

which are you graphing?

Answer 16

4sinx

Answer 17

so... is that right?

Answer 18

so does my original statement still stand?

Answer 19

at t = 3pi/4 the spring position function is positive, and the derivative of the position function is positive, so the spring is going up. however, the second derivative (which we didn't find, but you easily eyeball) is negative, so the spring is slowing down and will soon reverse.

Answer 20

ahh ok so i got it right, thanks a bunch

Answer 21

yeah, I just like making graphs :)