Question

The position of a particle is given by
s = 5 cos( 2t +90) at time t. What are the maximum values of the displacement, the velocity, and acceleration?

Answer 1

\[s=5\cos(2t +\frac{ \pi }{ 4 })\]

Answer 2

I just need help getting the maximum value of the displacement

Answer 3

maximum values of displacement occur when slope of the curve is equal to zero. so, take the derivative of your function, then set that equal to zero. the value of s, when solved, will be the 'maximum values of displacment'

Answer 4

okay thanks, I got t= -0.393 and when i plugged that into the function i got 5 which is right,
so to get the max values of velocity I would have to get the second derivative and then make equal to zero and once i get the values for t which function do i plug that number into?

Answer 5

"so to get the max values of velocity I would have to get the second derivative and then make equal to zero"

yep!

Answer 6

but which function would i have to plug "t" into?

Answer 7

maximum velocoity occurs when the slope is zero again, and the maximum acceleration occurs when the slope is zero, again, of the second and third derivatives respectivly

Answer 8

the second derivative function or the orignal function

Answer 9

so this is how things look:

d(position) = velocity
d(velocity) = acceleration

does that help, or did i misunderstand your quesiton?

Answer 10

Let me try and then if i dont get it ill come back to u