v(t) = 9t*t + 4t

at t=0, s=0

a) d s(t)/dt = 9t*t + 4t

=> s = (9*t*t*t/3 ) + 4t*t/2 +c

Now at t=0, s=0

Thus, 0=0+0+c => c = 0

Hence s(t) = 3t^3 + 2t^2 = t*t(3t+2)

b) after 2 s

s(t) = s(2) = 2*2(3*2+2) = 32 ft

c) s(10) -s(5) = 10*10(10*3+2) -5*5(5*3+2)

= 100*32 - 25*17

=2775 ft

Hence change in position from 5 to 10 s is 2775 ft

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