Understanding Derivatives in Scientific Calculations

[powp]

Hello

I am I finding the derivative for this right??

d = small delta

s(t) = A Cos(wt + d)


s'(t) = -A Sin(wt + d) * w

s'(t) = -Aw Sin(wt + d)

Is it correct to treat all the rest of the varibles as constants? My text does not give any examples with these.

All so what would make the velocity(s') = 0??

Thanks

Peter

 

[quasar987]

Hello
I am I finding the derivative for this right??
d = small delta
s(t) = A Cos(wt + d)
s'(t) = -A Sin(wt + d) * w
s'(t) = -Aw Sin(wt + d)
Is it correct to treat all the rest of the varibles as constants? My text does not give any examples with these.

Yep.

All so what would make the velocity(s') = 0??
Thanks
Peter

Well you got to ask yourself for what value(s) of t is s'(t) zero. To simplify the problem, make a change of variable y = wt + d. Find for what values of y is s'(y) zero, then find the corresponding values of t through t = (y-d)/w.

 

[powp]

Thanks.

So if I am not given any values for w,d, or A would I just state that the velocity is 0 when wt + d = 0?

 

[TD]

Thanks.
So if I am not given any values for w,d, or A would I just state that the velocity is 0 when wt + d = 0?

Is a sine only zero when the argument is zero?

 

[powp]

no it can be 0 at nPi. Is this correct?

 

[TD]

Indeed, sin(x) is 0 when x is [itex]k\pi[/tex] with k an integer.

 

[powp]

thanks for your help

 

[TD]

You're welcome