Hello taichi2910You are told:

and you are asked to find

- The value of the angular velocity - that's - when . So differentiate and plug in the value .

- The value of the angular acceleration - that's - when . Differentiate again, and put .

- The value of when . So use your equation in (2) and find the value of that will make the expression zero.

Can you do this now?

You have given us the equation . Are you sure this is correct? Should it be . This would certainly make more sense.water drain from a cylindrical tank of radius 4 meter. as the height h falls the pressure reduces and it is observer that the relationship h and time t is given by

h= 5e^t/21

find the rate that the heiht is falling after 3 s

the flow rate in liter persecond after 3 seconds

Whatever the formula, you need the rate that the height is falling - that's - when (and it should be negative - hence I suspect you have missed a minus sign).

So differentiate and put . This will give you the rate at which the height is falling in .

Then you need to convert this answer into a volume flow in l/sec. So find the cross-sectional area of the tank ( ), and multiply your first answer by this area. This will give the rate in . There are 1000 l in 1 . So divide by 1000.

Grandad