Solution:
1. AIr incoming rate =.25 cubic feet per second
Air capacity in 1 minute = Air incoming rate * time
=.25*60
=15 cubic feet of air
As we know that 1 cubic foot =.0283 cubic metre
hence Air capacity=15*.0283.4245 m^3
2. Air escape rate function r(t)=.25e-.05t
for t=30 sec
r(30)=.25e-.05*30
=7.1343 cubic feet
i.e =.0283*7.1343
=.2019 m^3
3 Air full capacity = 15 cubic feet of air
at t=45 sec
r(45)=.25e-.05*45
=10.7 cubic feet of air
Air remaining = 15-10.7
=4.2987 cubic feet of air
4 velocity function v(t)=45-32t
as we know that velocity is given by
v=ds/dt
thus
ds=v.dt
ds=(45-32t).dt
s= (45t-16t2)
=(45*3-16*3^2)-(45*02-16*0)
=-9 feet
5.
As s(0)=25
s=45t*16t^2+c
thus c=25
hence
s=45t-16t^2+25
at t=3
s=45*3-16*3^2+25
=16 feet
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