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

do you know the derivative of cosine?

Answer 2

-sin(x)

Answer 3

at 3pi/4 what does sine equal?

Answer 4

yes so in this case the derivative of \(-4\cos(x)\) is \(4\sin(x)\)

Answer 5

so the funtion is 4sin(x)|x = (3pi)/4
4sin((3pi/4) = 4(sqrt(2)/2) = 2sqrt(2)

Answer 6

I hateee these questions why does physics and math have to conflict on so many levels

Answer 7

how does in conflict?

Answer 8

replace \(x\) by \(\frac{3\pi}{4}\) and see what you get
that is the velocity
if it is positive, going up
if it is negative, going down

Answer 9

not in this case but however if you had a negative velocity

Answer 10

just means pointing down

Answer 11

negative vector is direction not value

Answer 12

and math doesn't take that into account however physics does and it bothersme

Answer 13

I dont understand what you are saying, a negative vector is fine in physics and mathematics

Answer 14

Physicists say that velocity cannot be negative it can only be zero or a positive magnitude from zero in a direction, where as mathematicians allow negative velocity, however it means that it is traveling in the oppositve direction

Answer 15

no it says speed cant be negative, speed = abs(velocity)

Answer 16

that's another way of saying it yes

Answer 17

speed is magnitude of vilocity

Answer 18

velociy is speed and it's direction, you cannot have a negative speed

Answer 19

but we use negative vilocity all over the place in physics
but its arbitrary because you can just flip the whole system in most cases, so sign is an indication of the origin of the axis which you supply

Answer 20

right velocity is speed and direction, and direction being negative says nothing about speed being negative.

Answer 21

if you hit a ball in the air and its falling and you are still on the ground its velocity is negative in respect to where you are, but if you rise to the vertex of where the ball went, and droped the ball so it took the same path down, the velocity is now positive with respect to where you are.

Answer 22

Velocity is a vector; speed is a scalar. A vector has a direction, a scalar does not.

If our problem is in a one-dimensional space, then we only have two possible directions; the sign, therefore, is used to denote the direction.

Answer 23

what if it is n-dimensional space

Answer 24

it still denotes direction with respect to origin

Answer 25

just the opposite direction of it being pos

Answer 26

just with 2d you can say up down, left, right...

Answer 27

-<1,1,1> points in the direction <-1,-1,-1>