we are given
[tex] v(t)=20+3cos(t) [/tex]
For finding distance , we will integrate v(t) from 0 to 25
[tex] distance=\int _0^{25}\left(20+3cos\left(t\right)\right)dt\: [/tex]
now, we can solve it
[tex] \int \:20+3\cos \left(t\right)dt [/tex]
[tex] =\int \:20dt+\int \:3\cos \left(t\right)dt [/tex]
[tex] =20t+3\sin \left(t\right) [/tex]
now, we can plug bounds
and we get
[tex] =500+3\sin \left(25\right)-0 [/tex]
[tex] =3\sin \left(25\right)+500 [/tex]
[tex] distance=499.60294feet [/tex]..............Answer
