Inversion will be your answer
To solve this problem it is necessary to apply the equations related to the description of the tangential and angular movement.
The displacement where the speed and acceleration is related is given by the equation:

Where
Initial velocity (0 because start from rest)
t = time
a = Acceleration
We have angular acceleration but not tangential acceleration. Tangential acceleration can be obtained through the relationship



And we have also that the displacement is

Now replacing,




Therefore will take the cord to unwind around 10s
Are
you familiar with that?
P = Momentum
M = Mass
t = time
v = velocity (speed)
J= Impulse
1.)
F = 100N
t = 5s
Change in momentum(P) = Ft
I see that this is not one of your equations but your equations do not work with this problem.
P = Ft
P = (100)(5)
P = 500 Ns
2.)
See if you can get this one by yourself from what I did on the last problem.
3.)
P = 25 kgm/s
M = 2.0 kg
So, you are looking for velocity (speed). Look for the equation that has momentum, mass and velocity.
Use the equation P = mv
25 = 2(v)
25 = 2v
25/ 2 = 2v/2
12.5 m/s = v
4.) Do the same for number 4.
P = 12 kgm/s
M = 1kg
P = mv
12 = 1v
12/1 = 1v/1
12 m/s = v
6.)
P = 100 kgm/s
V= 7.0m/s
P= mv
100 = m7.0
100/7 = 7.0m/7
14.28 kg = m
Try page 2 by yourself and message me or comment if you need more help. Just identify the variable you have and what you need to find and put them in an equation that fits. You can do this!!!!