I need help with this assignment questions problem 5 the ang

I need help with this assignment questions

problem 5

the angular acceleration of rotating object is is given by

= o-Cw, with o and C beign constant (note this symbol stand for alpha )

a: write an expression for dt/dw, than integrate t=w,o dt/dw

b: you got t as a fuction of w, insert it to get w as a fuction of time

c: what is lim w(t) if o= 20 rad/s2 and C=2/s

question 6

A proton collides head-on with a deuteron, intially stationary. The mass are m and 2m. the protons initial speed is Vo=30km/s

a: calculate both particles final speeds

b: calculate the intial momentum and kinetic energy( keep m as a variable, or call m a unit and use m instead of kg. Dont give any answers in Joules)

c: calculate the final momentum and kintic energy

a = a0 - Cw

and dw/dt = a = a0 - Cw

dw / (a0 - Cw) = dt

- ln(a0 - Cw) / C = t

w is from 0 to w

then

- [ ln(a0 - Cw) - ln(a0)] / C = t

t = - ln((a0 -Cw) /a0 ) / C

b) - Ct = ln((a0 -Cw) /a0 )

e^(-Ct) = (a0 - Cw) / a0

a0 - Cw = a0 e^(-Ct)

w =(a0/c) [ 1 - e^(-Ct ) ]

c) putting values,

w = (20 / 2) [ 1 - e^(-2t)]

w(t) = 10 [ 1 - e^(-2t)] rad /s